Exhibit 10.5

WARRANT SOLICITATION AGENT AGREEMENT

THIS WARRANT SOLICITATION AGENT AGREEMENT (this “Agreement”) is dated as of July 10, 2026, by and between Matinas BioPharma Holdings, Inc. (the “Company”) and ThinkEquity LLC (“ThinkEquity” or the “Solicitation Agent”).

RECITALS

WHEREAS, pursuant to certain prior offerings, the Company issued to the holders of certain existing warrants(the “Holders”), among others, common stock purchase warrants to purchase the number of shares of the Company’s common stock, par value $0.0001 per share (“Common Stock”), set forth opposite of such Holder’s name, at an initial exercise price of $0.6446 per share, subject to adjustment as provided therein (the “Existing Warrants”);

WHEREAS, based on certain anti-dilution adjustments that will occur immediately prior to the closing of the transactions contemplated hereunder it is anticipated that the exercise price of the Existing Warrants will be adjusted to $0.35 per share (the “Current Exercise Price”)

WHEREAS, the Company desires to offer the Holders the opportunity to exercise their outstanding Existing Warrants for shares of Common Stock at the Current Exercise Price during the Inducement Period (as defined below), and in consideration for each Existing Warrant exercised, the Company will issue to the participating Holders a new warrant (each, a “New Warrant” and, collectively, the “New Warrants”) to purchase an equal number of shares of Common Stock as the number of shares issued upon exercise of the Existing Warrants, in each case subject to the terms and conditions set forth in an Inducement Offer Letter between the Company and each Holder (collectively, the “Inducement Offer Letters”); and

WHEREAS, the Company desires to engage the Solicitation Agent to act on its behalf, and the Solicitation Agent is willing to serve, as the exclusive warrant solicitation agent for the above-described transactions (the “Warrant Transaction”) on the terms and conditions set forth herein.

NOW, THEREFORE, in consideration of the premises and the mutual agreements herein set forth, the parties hereto agree as follows:

1. Appointment of Warrant Solicitation Agent. The Company hereby appoints ThinkEquity, and ThinkEquity hereby agrees to serve, as the exclusive warrant solicitation agent for the Warrant Transaction. The Company hereby represents and warrants that the list of the Holders set forth on Exhibit A attached hereto, including the number of shares of Common Stock issuable upon exercise of outstanding Existing Warrants held by the Holders, are the only holders of Existing Warrants subject to the Warrant Transaction (the “Existing Warrant Holder List”), and such Existing Warrant Holder List is true, correct and complete.

The Solicitation Agent shall, consistent with its obligations under applicable laws and the rules and regulations of the Financial Industry Regulatory Authority (“FINRA”) and the Securities and Exchange Commission (the “Commission”), use its commercially reasonable efforts to maximize the number of Existing Warrants which are exercised. In connection therewith, the services to be provided by the Solicitation Agent shall consist of the following:

(a) use of its commercially reasonable efforts to contact the Holders to inform them of the Company’s decision to pursue the Warrant Transaction, including informing them of the deadline for exercising the Existing Warrants at the Current Exercise Price in consideration of the receipt of New Warrants;

(b) assisting the Holders in the processing of their Existing Warrant exercises in a timely manner, including answering any questions by the Holders concerning the procedure for exercising their Existing Warrants for Common Stock, receiving New Warrants, confirming that the exercise notices have been properly executed by the Holders and, if requested, forwarding of the executed exercise notices to the Company, together with the exercise payment; and

(c) provide the Company with periodic updates during the Inducement Period (as defined below) of the Holders contacted by the Solicitation Agent, including whether such Holders indicated their intention to exercise their Existing Warrants during the Inducement Period and any other questions or information requests made by such Holders.

2. Warrant Solicitation Fee.

(a) Amount of Solicitation Fee. The Company shall pay the Solicitation Agent a fee (the “Warrant Solicitation Fee”) consisting of: (i) a cash payment equal to ten percent (10%) of the total gross cash proceeds received by the Company from all exercises of Existing Warrants that occur on or prior the Execution Time (as such term is defined in the Inducement Offer Letters (hereinafter, the “Inducement Period”), which Inducement Period may be extended as further set forth in the Inducement Offer Letters; and (ii) warrants (the “Solicitation Agent Warrants”) to purchase a number of shares of Common Stock equal to five percent (5%) of the aggregate number of New Warrants issued to the Holders in connection with the transactions contemplated by the Inducement Offer Letters. The Solicitation Agent Warrants shall have an exercise price of $0.35 per share (or such other exercise price as is applicable to the New Warrants) and otherwise shall have substantially the same terms and conditions as the New Warrants, except as necessary to comply with applicable FINRA rules and regulations. The Company shall determine, in consultation with the Solicitation Agent, whether a Holder properly exercised its Existing Warrant(s) during the Inducement Period. The Company confirms to the Solicitation Agent that the shares of Common Stock issuable upon exercise of the Existing Warrants are subject to effective resale registration statements on file with the Commission (SEC File No. 333-286686).

(b) Closing; Payment of Solicitation Fee and Issuance of Solicitation Agent Warrants. During the Inducement Period and upon request, the Company shall provide the Solicitation Agent with an updated list of Holders who have exercised Existing Warrants during the Inducement Period and the number of New Warrants issued or issuable in connection therewith. A single closing (the “Closing”) with respect to all exercises of Existing Warrants consummated during the Inducement Period shall be held no later than two (2) Trading Days following the expiration of the Inducement Period. At the Closing, the Company shall (i) pay to the Solicitation Agent the cash portion of the Warrant Solicitation Fee attributable to all exercises consummated during the Inducement Period, (ii) issue to the Solicitation Agent the applicable number of Solicitation Agent Warrants earned in connection therewith, and (iii) pay the Expense Reimbursement (as defined below).

(c) Entire Solicitation Fee. The amounts to be paid to the Solicitation Agent under Section 2(a) above, together with the reasonable legal and other expenses of the Solicitation Agent (the “Expense Reimbursement”); provided, however, that the aggregate amount of Expense Reimbursement payable by the Company to the Solicitation Agent in connection with (i) this Agreement and (ii) a separate financing transaction of the Company for which the Solicitation Agent previously provided services but is not participating in at the date hereof, shall not exceed $50,000 in the aggregate, unless otherwise agreed to in writing by the Company and the Solicitation Agent.

3. Representations, Warranties and Covenants of the Company. The Company represents, warrants and covenants as follows:

(a) The Company is a corporation duly organized, validly existing and in good standing under the laws of the State of Delaware and has full corporate power and authority to execute and deliver this Agreement and to consummate the transactions contemplated hereby. All corporate proceedings on the part of the Company necessary to authorize this Agreement and the transactions contemplated hereby, including, without limitation, the issuance of New Warrants for Holders who exercise Existing Warrants, have been duly and validly taken and no further action is required by the Company, the Board of Directors or the Company’s stockholders in connection herewith. This Agreement has been duly and validly authorized, executed and delivered by the Company, constitutes the legal, valid and binding agreement and obligation of the Company, enforceable against it in accordance with its terms, except as enforceability may be limited by bankruptcy, insolvency, moratorium or other similar laws affecting creditors’ rights generally, including, without limitation laws regarding fraudulent or preferential transfers, or by the principles governing the availability of equitable remedies.

(b) The shares of Common Stock underlying the Existing Warrants and New Warrants have been duly authorized, have been duly reserved for issuance and upon exercise of the Existing Warrants and the New Warrants and the payment to the Company of the exercise price therefor, such shares of common stock shall be validly issued, fully paid and non-assessable.

(c) Neither the execution and delivery of this Agreement by the Company nor the consummation of the transactions contemplated hereby will (i) conflict with or result in any breach of any provision of the Certificate of Incorporation or Bylaws of the Company, each as amended to date; (ii) require any consent, approval, authorization or permit from, or filing with or notification to, any United States or foreign governmental or regulatory authority or other third party, except for any such consents, approvals, authorizations, permits, filings or notifications, the absence of which could not have or reasonably be expected to result in: (1) a material adverse effect on the legality, validity or enforceability of this Agreement; (2) a material adverse effect on the results of operations, assets, business, prospects or condition (financial or otherwise) of the Company and its subsidiaries, taken as a whole; or (3) a material adverse effect on the Company’s ability to perform in any material respect on a timely basis its obligations under this Agreement or the Inducement Offer Letters (any of (1), (2) or (3), a “Material Adverse Effect”); (iii) result in a breach of the terms, conditions or provisions of, constitute a default (or an event which, upon notice or lapse of time or both, would constitute a default) under or cause, permit or give rise to any right of termination, cancellation or acceleration under any of the terms, conditions or provisions of any material agreement or other material instrument or obligation to which the Company is a party or by which the Company is bound; (iv) conflict with or result in a violation of any provision of any statute, rule, regulation, order or judgment applicable to the Company, including applicable federal or state securities laws, which conflict or violation would reasonably be expected to have a Material Adverse Effect; (v) the offer, issuance and sale of the securities contemplated by the Inducement Offer Letters, and the solicitation activities contemplated hereby as conducted in accordance therewith, will not violate any applicable federal or state securities laws in any material respect; and (vi) no filing, disclosure or reporting obligation is required to be made by the Company in connection with the transactions contemplated hereby, other than those expressly contemplated by the Inducement Offer Letters or the failure of which to make would not reasonably be expected to have a Material Adverse Effect.

(d) The Company has filed all reports, schedules, forms, statements and other documents required to be filed by the Company under the Securities Act of 1933, as amended, and the rules and regulations promulgated thereunder (“Securities Act”), and the Securities Exchange Act of 1934, as amended, and the rules and regulations promulgated thereunder (“Exchange Act”), including pursuant to Section 13(a) or 15(d) thereof, for the two years preceding the date hereof (the foregoing materials, including the exhibits thereto and documents incorporated by reference therein, being collectively referred to herein as the “SEC Reports”) on a timely basis or has received a valid extension of such time of filing and has filed any such SEC Reports prior to the expiration of any such extension. As of their respective dates, the SEC Reports complied in all material respects with the requirements of the Securities Act and the Exchange Act, as applicable, and none of the SEC Reports, when filed, contained any untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading. The Company has never been an issuer subject to Rule 144(i) under the Securities Act. The financial statements of the Company included in the SEC Reports comply in all material respects with applicable accounting requirements and the rules and regulations of the Commission with respect thereto as in effect at the time of filing. Such financial statements have been prepared in accordance with United States generally accepted accounting principles applied on a consistent basis during the periods involved (“GAAP”), except as may be otherwise specified in such financial statements or the notes thereto and except that unaudited financial statements may not contain all footnotes required by GAAP, and fairly present in all material respects the financial position of the Company and its consolidated Subsidiaries as of and for the dates thereof and the results of operations and cash flows for the periods then ended, subject, in the case of unaudited statements, to normal, immaterial, year-end audit adjustments.

(e) Since the date of the latest audited financial statements included within the SEC Reports, (i) there has been no event, occurrence or development that has had or that could reasonably be expected to result in a Material Adverse Effect, (ii) the Company has not incurred any liabilities (contingent or otherwise) other than (A) trade payables and accrued expenses incurred in the ordinary course of business consistent with past practice and (B) liabilities not required to be reflected in the Company’s financial statements pursuant to GAAP or disclosed in filings made with the Commission, (iii) the Company has not altered its method of accounting, (iv) the Company has not declared or made any dividend or distribution of cash or other property to its stockholders or purchased, redeemed or made any agreements to purchase or redeem any shares of its capital stock and (v) the Company has not issued any equity securities to any officer, director or Affiliate, except pursuant to existing Company stock option plans. The Company does not have any request before the Commission for confidential treatment of information.

(f) The Company: (i) is not in default under or in violation of (and no event has occurred that has not been waived that, with notice or lapse of time or both, would result in a default by the Company), nor has the Company received notice of a claim that it is in default under or that it is in violation of, any indenture, loan or credit agreement or any other agreement or instrument to which it is a party or by which it or any of its properties is bound (whether or not such default or violation has been waived), (ii) is not in violation of any judgment, decree or order of any court, arbitrator or other governmental authority or (iii) is not or has not been in violation of any statute, rule, ordinance or regulation of any governmental authority, including without limitation all foreign, federal, state and local laws relating to taxes, environmental protection, occupational health and safety, product quality and safety and employment and labor matters, except in each case as could not have or reasonably be expected to result in a Material Adverse Effect.

(g) The Common Stock is registered pursuant to Section 12(b) or 12(g) of the Exchange Act, and the Company has taken no action designed to, or which to its knowledge is likely to have the effect of, terminating the registration of the Common Stock under the Exchange Act nor has the Company received any notification that the Commission is contemplating terminating such registration. Except as set forth in the SEC Reports, the Company has not, in the 12 months preceding the date hereof, received notice from any Trading Market (as defined below) on which the Common Stock is or has been listed or quoted to the effect that the Company is not in compliance with the listing or maintenance requirements of such Trading Market. The Company is and has no reason to believe that it will not in the foreseeable future continue to be, in compliance with all such listing and maintenance requirements. The Common Stock is currently eligible for electronic transfer through the Depository Trust Company or another established clearing corporation and the Company is current in payment of the fees to the Depository Trust Company (or such other established clearing corporation) in connection with such electronic transfer. “Trading Market” means any of the following markets or exchanges on which the Common Stock is listed or quoted for trading on the date in question: the NYSE American, the Nasdaq Capital Market, the Nasdaq Global Market, the Nasdaq Global Select Market, the New York Stock Exchange, OTCQB or OTCQX (or any successors to any of the foregoing).

(h) The transactions contemplated under the Inducement Offer Letters comply with all the rules and regulations of the NYSE American.

(i) Except for fees payable by the Company to the Solicitation Agent, no brokerage or finder’s fees or commissions are or will be payable by the Company to any broker, financial advisor or consultant, finder, placement agent, investment banker, bank or other person or entity with respect to the transactions contemplated by the Warrant Transaction or this Agreement.

(j) During the Inducement Period, the Company shall comply in all material respects with the Securities Act, the Exchange Act, the rules and regulations of the Commission, and the rules of the NYSE American, and shall timely file all reports and disclosures required to be filed thereunder.

(k) The Company shall promptly notify the Solicitation Agent of (i) any material development relating to the Company or the Warrant Transaction, (ii) any trading halt, suspension or delisting notice relating to the Common Stock, or (iii) any inquiry, investigation or request for information from the Commission, FINRA or the NYSE American relating to the Warrant Transaction.

4. Representations and Warranties of the Solicitation Agent. The Solicitation Agent represents and warrants as follows:

(a) The Solicitation Agent is a corporation duly organized, validly existing and in good standing under the laws of its jurisdiction of organization and has all requisite corporate power and authority to execute and deliver this Agreement and to perform its obligations hereunder. The Solicitation Agent is a registered broker-dealer and a member of FINRA. All corporate proceedings on the part of the Solicitation Agent necessary to authorize the execution, delivery and performance of this Agreement have been duly and validly taken. This Agreement has been duly authorized, executed and delivered by the Solicitation Agent and constitutes a valid and binding obligation of the Solicitation Agent, enforceable against it in accordance with its terms, except as enforceability may be limited by bankruptcy, insolvency, moratorium or other similar laws affecting creditors’ rights generally, including, without limitation laws regarding fraudulent or preferential transfers, or by the principles governing the availability of equitable remedies.

5. Indemnification. The parties acknowledge and agree that the indemnification, reimbursement of fees and expenses, contribution and related provisions set forth in Section H of that certain Engagement Letter Agreement, dated June 10, 2026, by and between the Company and ThinkEquity LLC, as amended July 2, 2026 (the “Engagement Letter”) are hereby incorporated into this Agreement by reference mutatis mutandis as though fully set forth herein and shall apply to the Warrant Solicitation, this Agreement and the services provided by the Solicitation Agent hereunder with the same force and effect as if expressly set forth in this Agreement.

6. Termination. Notwithstanding anything in this Agreement to the contrary, this Agreement shall terminate at the end of the Inducement Period (and following the payment of all fees and expenses due to the Solicitation Agent hereunder) and also may be terminated at any time and for any reason by either the Company or the Solicitation Agent if either party shall default in the performance of its obligations under this Agreement and the defaulting party shall not have cured the same within five (5) business days after the receipt of written notice from the non-defaulting party specifying such default, at which time the termination shall be effective. If this Agreement is terminated pursuant to this Section 6, this Agreement shall thereafter have no effect except for (i) the Company’s obligation to pay the Warrant Solicitation Fee for exercises of Existing Warrants prior to the effectiveness of said termination and to reimburse expenses of the Solicitation Agent as provided herein and (ii) both parties’ indemnification obligations under Section 5 above, all of which shall survive the termination of this Agreement. Notwithstanding the foregoing, the Solicitation Agent may terminate this Agreement immediately upon written notice to the Company after consultation with the Company if continued performance hereunder could reasonably be expected to result in a violation of applicable securities laws or the rules or regulations of FINRA or the Commission.

7. Miscellaneous.

(a) Survival of Representations and Warranties. The parties’ respective representations and warranties contained in this Agreement shall survive until one year after the termination of this Agreement; provided, however, that the indemnification obligations set forth in Section 5 shall survive in accordance with their terms.

(b) Amendment and Waiver. Any term or provision of this Agreement may be waived at any time by the party which is entitled to the benefits thereof, but only in a writing signed by such party, and this Agreement may be amended or supplemented at any time, but only by written agreement of the Company and Solicitation Agent. Any such waiver with respect to a failure to observe any such provision shall not operate as a waiver of any subsequent failure to observe such provision unless otherwise expressly provided in such waiver.

(c) Expenses. Except as otherwise provided in this Agreement, the Company and Solicitation Agent shall pay their respective fees, commissions, costs, and other expenses, separately incurred in connection with the preparation and execution of this Agreement and the consummation of the transactions contemplated hereby.

(d) Entire Agreement. This Agreement contains the entire agreement between the Company and Solicitation Agent with respect to the solicitation of the exercise of the Existing Warrants and supersedes all prior arrangements or understandings with respect thereto provided, however, that notwithstanding anything herein to the contrary, the provisions of Sections B, C, D and H of the Engagement Letter, shall survive the execution and delivery of this Agreement and the consummation or termination of the transactions contemplated hereby and shall remain in full force and effect in accordance with their terms., and there have been no oral representations or warranties and neither party has relied on any representation not contained herein.

(e) Notices. All notices, consents, requests, instructions, approvals and other communications provided for herein shall be validly given, made or served, if in writing and delivered personally or sent by fax (except for legal process) or certified mail, postage prepaid, to: Any and all notices or other communications or deliveries required or permitted to be provided hereunder shall be in writing and shall be deemed given and effective on the earliest of: (a) the time of transmission, if such notice or communication is delivered via email at the email address as set forth below at or prior to 5:30 p.m. (New York City time) on a business day, (b) the next business day after the time of transmission, if such notice or communication is delivered via email at the email address as set forth below on a day that is not a business day or later than 5:30 p.m. (New York City time) on any business day, (c) the second (2nd) business day following the date of mailing, if sent by U.S. nationally recognized overnight courier service or (d) upon actual receipt by the party to whom such notice is required to be given. The address for such notices and communications shall be as set forth below, which may be revised to such other address or email address as any party hereto may, from time to time, designate in a written notice given in a like manner.

Company:

Matinas BioPharma Holdings, Inc.

1545 Route 206 South, Suite 302

Bedminster, New Jersey 07921

Attn: Jerome D. Jabbour, CEO

E-Mail: [*]

With copies to:

Lowenstein Sandler

1251 Avenue of the Americas

New York, New York 10020

Attn: Steven M. Skolnick, Esq.

E-Mail: sskolnick@lowenstein.com

ThinkEquity LLC

17 State Street, 41^st floor

New York, NY 10004

Attn: Eric Lord, Head of Investment Banking

Email: [*]

With copies to:

Littman Krooks LLP

1325 Avenue of the Americas 15th Floor

New York, NY 10019

Attn: Steven D. Uslaner, Esq.

Email: suslaner@littmankrooks.com

(f) Assignment. This Agreement may not be assigned, by operation of law or otherwise, and any attempt to do so shall be void. This Agreement shall be binding upon and inure to the benefit of successors and assigns of the parties hereto.

(g) Counterparts. This Agreement may be executed in one or more counterparts, each of which shall be deemed to be an original, but all of which together shall constitute one and the same instrument. Any such counterpart, to the extent delivered by means of a facsimile machine or by .pdf, .tif, .gif, .jpeg or similar attachment to electronic mail (any such delivery, an “Electronic Delivery”) shall be treated in all manner and respects as an original executed counterpart and shall be considered to have the same binding legal effect as if it were the original signed version thereof delivered in person. At the request of any party hereto, each other party hereto or thereto shall re- execute the original form of this Agreement and deliver such form to all other parties. No party hereto shall raise the use of Electronic Delivery to deliver a signature or the fact that any signature or agreement or instrument was transmitted or communicated through the use of Electronic Delivery as a defense to the formation of a contract, and each such party forever waives any such defense, except to the extent such defense relates to lack of authenticity.

(h) APPLICABLE LAW, COSTS, ETC. This Agreement will be governed by, construed and enforced in accordance with the laws of the state of New York applicable to contracts made and to be performed wholly within such state. The parties hereto hereby irrevocably submit to the jurisdiction of any New York State or United States federal court sitting in New York County over any action or proceeding arising out of or relating to this Agreement or any agreement contemplated hereby, and the parties hereto hereby irrevocably agree that all claims in respect of such action or proceeding shall be heard and determined in such New York State or federal court. The parties hereto further waive any objection to venue in such state and any objection to an action or proceeding in such state on the basis of a non-convenient forum. The parties hereto further agree that any action or proceeding brought against each other shall be brought only in New York State or United States federal courts sitting in New York County. The Company and the Solicitation Agent each hereby waives its right to a jury trial of any claim or cause of action based upon or arising out of this Agreement or any document or agreement contemplated hereby. The Solicitation Agent or the Company, as the case may be, shall be entitled to costs and reasonable attorney’s fees in the event it prevails in any claims, actions, awards or judgment under this agreement.

(i) Construction of Agreement. Each of the parties hereto acknowledges and agrees that no provision in this Agreement is to be interpreted for or against any party because that party or that party’s legal representative drafted the provision.

(j) Liability Limitation. In no event shall the Solicitation Agent be liable to the Company for any indirect, incidental, consequential, punitive or special damages arising out of or relating to this Agreement.

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed as of the date and year first above written.

MATINAS BIOPHARMA HOLDINGS, INC.

THINKEQUITY LLC

Exhibit A

Existing Warrant Holder List