Exhibit 5.1

July 10, 2026

Corvex, Inc.

3401 North Fairfax Drive, Suite 3230

Arlington, Virginia 22226

Ladies and Gentlemen:

We have acted as counsel to Corvex, Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-1 filed on the date hereof (including the prospectus forming a part thereof, the “Registration Statement”) with the U.S. Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), to register the offer and resale by those stockholders of the Company listed in the Registration Statement under the heading “Selling Stockholders” (collectively, the “Selling Stockholders” and each, a “Selling Stockholder”) of up to an aggregate of 53,390,008 shares of the Company’s common stock, par value $0.0001 per share (“Common Stock”) consisting of: (i) 389,623 shares of Common Stock previously issued upon conversion of the Company’s Series A Convertible Preferred Stock, par value $0.0001 per share of the Company (“Series A Preferred Stock”), pursuant to the Series A Certificate of Designations (as defined below), which shares of Series A Preferred Stock were issued pursuant to (A) the Preferred Stock Subscription Agreement, dated November 5, 2025, made and entered into by and among the Company and MACN Ventures LLC and (B) the Preferred Stock Subscription Agreement, dated November 5, 2025, made and entered into by and among the Company and Policy Pros Corp. (together, the “Series A Subscription Agreements”); (ii) 236,008 shares of Common Stock previously issued upon conversion of the Company’s Series B Convertible Preferred Stock, par value $0.0001 per share (“Series B Preferred Stock”), pursuant to the Series B Certificate of Designations (as defined below), which shares of Series B Preferred Stock were issued pursuant to the Amended and Restated Agreement and Plan of Merger, dated March 19, 2026, by and among the Company, Thor Merger Sub Inc., a Delaware corporation and a wholly-owned subsidiary of the Company, and Corvex Legacy Holdings, Inc. (the “Merger Agreement”); (iii) 19,082,545 shares of Common Stock previously issued upon conversion of the Company’s Series C Non-Voting Convertible Preferred Stock, par value $0.0001 per share (“Series C Preferred Stock”), pursuant to the Series C Certificate of Designations (as defined below), which shares of Series C Preferred Stock were issued pursuant to the Merger Agreement; (iv) 4,752,244 shares of Common Stock previously issued upon conversion of the Company’s Series D Non-Voting Convertible Preferred Stock, par value $0.0001 per share (“Series D Preferred Stock”), pursuant to the Series D Certificate of Designations (as defined below), which shares of Series D Preferred Stock were issued pursuant to the Merger Agreement; and (v) up to 28,929,588 shares of Common Stock issuable upon conversion of currently outstanding shares of Series D Preferred Stock pursuant to the Series D Certificate of Designations, which shares of Series D Preferred Stock were issued pursuant to (A) the Merger Agreement, (B) the Exchange Agreement entered into as of July 1, 2026 by and between the Company and Moira Partners LLC, (C) the Exchange Agreement entered into as of July 1, 2026 by and between the Company and Goldbrook Corvex Holdings II, LLC, (D) the Exchange Agreement entered into as of July 1, 2026 by and between the Company and Goldbrook Klustr Holdings, LLC, (E) the Exchange Agreement entered into as of July 1, 2026 by and between the Company and Chardan Capital Markets, LLC, (F) the Exchange Agreement entered into as of July 1, 2026 by and between the Company and Go Klustr LLC, (G) the Exchange Agreement entered into as of July 1, 2026 by and between the Company and Avico II LLC, or (H) the Exchange Agreement entered into as of July 1, 2026 by and between the Company and Chardan Holdings, LP (the Exchange Agreements reflected in the foregoing clauses (B) through (H) are collectively referred to as the “Exchange Agreements”). The shares of Common Stock referenced in clauses (i) through (iv) above are referred to herein collectively as the “Shares” and each, a “Share”, and the shares of Common Stock referenced in clause (v) above are referred to herein as the “Conversion Shares” and each, a “Conversion Share”.

Corvex, Inc.

July 10, 2026

Page 2

This opinion letter is being furnished to you in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

You have requested our opinion as to the matters set forth below in connection with the Registration Statement and the offering of the Shares thereunder. For purposes of rendering those opinions, we have examined (collectively, the “Reviewed Documents”): (i) the Registration Statement; (ii) the Series A Subscription Agreements; (iii) the Merger Agreement; (iv) the Exchange Agreements; (v) the Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State of the State of Delaware (the “Secretary of State”) on March 24, 2021, as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on June 21, 2023, as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on July 9, 2024, as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on October 25, 2024 and effective as of 12:01 a.m. Eastern Time on October 29, 2024, as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on October 8, 2025 and effective as of 12:01 a.m. Eastern Time on October 10, 2025, as amended by the Certificate of Designations of Series A Convertible Preferred Stock of the Company as filed with the Secretary of State on November 6, 2025 (the “Series A Certificate of Designations”), as amended by the Certificate of Designations of Series B Convertible Preferred Stock of the Company as filed with the Secretary of State on March 19, 2026 (the “Series B Certificate of Designations”), as amended by the Certificate of Designations of Series C Non-Voting Convertible Preferred Stock of the Company as filed with the Secretary of State on March 19, 2026 (the “Series C Certificate of Designations”), as amended by the Certificate of Designations of Series D Non-Voting Convertible Preferred Stock of the Company as filed with the Secretary of State on March 19, 2026 (the “Series D Certificate of Designations”), as amended by the Certificate of Amendment of Third Amended and Restated Certificate of Incorporation of the Company as filed with the Secretary of State on March 19, 2026 and effective as of 12:01 a.m. Eastern Time on March 23, 2026, and as amended by the Certificate of Increase of Series D Non-Voting Convertible Preferred Stock of the Company as filed with the Secretary of State on July 1, 2026 (collectively, the “Certificate of Incorporation”); (vi) the Second Amended and Restated Bylaws of the Company adopted effective as of March 23, 2026 (the “Bylaws” and together with the Certificate of Incorporation, the “Organizational Documents”); (vii) the resolutions adopted by the Board of Directors of the Company (the “Board of Directors”) on November 3, 2025, approving, among other things, the issuance of shares of Series A Preferred Stock pursuant to the Series A Subscription Agreements (the “November Board Resolutions”); (viii) the resolutions adopted by the Board of Directors on March 19, 2026, approving, among other things, the issuance of shares of Series A Preferred Stock pursuant to the Series A Subscription Agreements and shares of Series B Preferred Stock, Series C Preferred Stock, and Series of D Preferred Stock pursuant to the Merger Agreement (the “March Board Resolutions”); (ix) the resolutions adopted by the Board of Directors on June 25, 2026, approving, among other things, the issuance of shares of Series D Preferred Stock pursuant to the Exchange Agreements (the “June Board Resolutions”); and (x) a certificate of an officer of the Company, dated as of the date hereof, with respect to certain matters. Other than our examination of the Reviewed Documents, we have not examined any other documents or made any independent investigation for the purpose of rendering this opinion.

Corvex, Inc.

July 10, 2026

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For purposes of rendering our opinions in the numbered paragraphs below, we have not examined any document other than the Reviewed Documents and assume there exists no provision in any document relating to the matters covered by our opinion below that we have not examined that is inconsistent with the Reviewed Documents or our opinion below. We have conducted no independent factual investigation of our own but rather have relied on the Reviewed Documents, the statements and information set forth therein, and the additional matters recited or assumed herein, all of which we assume to be true, complete, and accurate in all respects.

For purposes of rendering our opinions in the numbered paragraphs below, we have made assumptions that are customary in opinion letters of this kind, including the assumptions that: (a) each of the Reviewed Documents is accurate and complete; (b) each of the Reviewed Documents that is an original is authentic; (c) each of the Reviewed Documents that is a copy conforms to an authentic original; (d) all signatures on each of the Reviewed Documents are genuine; and (e) there are no documents other than the Reviewed Documents that could affect the opinions expressed in the numbered paragraphs below and no amendments, modifications, or waivers of the Reviewed Documents. We have further assumed (i) the legal capacity of natural persons, (ii) that each party to the Reviewed Documents (A) is duly formed or incorporated, as applicable, organized, validly existing, and in good standing under the laws of the state of its formation or incorporation, as applicable, (B) has the legal capacity, power, and authority to execute, deliver, and perform its obligations under the Reviewed Documents to which it is a party, (C) has taken all action necessary to duly authorize the execution and delivery of, and the performance of such party’s obligations under, the Reviewed Documents, and (D) has duly executed and delivered the Reviewed Documents, (iii) the Reviewed Documents constitute the legal, valid, and binding obligation of each party thereto, enforceable against each such party in accordance with their terms, (iv) the Company is and shall remain at all times a corporation duly incorporated, validly existing, and in good standing under the laws of the State of Delaware, and (v) any amendment, restatement, or amendment and restatement or assumption of the Reviewed Documents was accomplished in accordance with, and was permitted by, the relevant provisions of such document and applicable law. We have not verified any of the foregoing assumptions.

Corvex, Inc.

July 10, 2026

Page 4

In rendering our opinions in the numbered paragraphs below, we also have assumed that (i) the Company will have sufficient authorized, unissued, and unreserved shares of Common Stock available for issuance of the Conversion Shares in accordance with the Series D Certificate of Designations, (ii) that the issuance of each Conversion Share will be duly recorded in the Company’s stock ledger upon issuance, (iii) in accordance with Section 158 of the General Corporation Law of the State of Delaware (the “DGCL”), either (A) upon the issuance of a Conversion Share, such Conversion Share will be evidenced by a certificate that has been duly executed and delivered, or (B) the Board of Directors will have adopted resolutions providing that all shares of Common Stock shall be uncertificated prior to the issuance of the Conversion Shares and, within a reasonable time after the issuance of any such Conversion Share, the registered owner of such Conversion Share will be given notice in writing or by electronic transmission in compliance with Section 151(f) of the DGCL, (iv) other than those that have been disclosed by the Company in filings made by the Company with the Commission since January 1, 2020, there are no contracts with one or more current or prospective stockholders of the Company (or one or more beneficial owners of stock of the Company), in its or their capacity as such, within the meaning of Section 122(18) of the DGCL, (v) the issuance of the shares of Series A Preferred Stock pursuant to the Series A Subscription Agreements, the shares of Series B Preferred Stock, Series C Preferred Stock, and Series D Preferred Stock pursuant to the Merger Agreement, and the shares of Series D Preferred Stock pursuant to the Exchange Agreements did not, and the issuance of the Conversion Shares in accordance with the Series D Certificate of Designations will not, (A) have the effect, directly or indirectly, of increasing the proportionate share of the stock of any class or series, or securities convertible into the stock of any class or series, of the Company held by an interested stockholder (within the meaning of Section 203(c) of the DGCL) or (B) confer a benefit, directly or indirectly (except proportionately as a stockholder of the Company) of any loans, advances, guarantees, pledges, or other financial benefits (other than those expressly permitted in paragraphs (c)(3)(i)-(iv) of Section 203 of the DGCL) on an interested stockholder (within the meaning of Section 203(c) of the DGCL), (vi) the issuance of the Conversion Shares in accordance with the Series D Certificate of Designations to any holder thereof will not result in such holder and its Affiliates, and any other person acting as a group (determined in accordance with Section 13(d) of the Securities Exchange Act of 1934 and the rules and regulations promulgated thereunder) together with such Selling Stockholder and its Affiliates, beneficially owning in excess of the Beneficial Ownership Limitation (as defined in the Series D Certificate of Designations), (vii) the November Board Resolutions, the March Board Resolutions and the June Board Resolutions (together, the “Board Resolutions”) have not been, and the Board Resolutions will not be, in each case, revoked, modified, or amended, and (viii) each share of Series A Preferred Stock, Series B Preferred Stock, Series C Preferred Stock, and Series D Preferred Stock converted into the Shares pursuant to the Series A Certificate of Designations, Series B Certificate of Designations, Series C Certificate of Designations, and Series D Certificate of Designations, as applicable, were duly issued, fully paid, and non-assessable. We have not verified any of the foregoing assumptions.

Our opinions set forth in the numbered paragraphs below are limited to the DGCL and reported judicial decisions interpreting the DGCL. We express no opinion as to the laws, rules, or regulations of any other jurisdiction, including, without limitation, the federal laws of the United States of America or any state securities or blue sky laws; we express no opinion with respect to the Corporate Transparency Act.

Corvex, Inc.

July 10, 2026

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Based upon and subject to the foregoing, it is our opinion that:

1. the Shares have been duly authorized and are validly issued, fully paid, and non-assessable; and

2. the Conversion Shares are duly authorized for issuance by the Company and, when issued upon the conversion of shares of Series D Preferred Stock in accordance with the Series D Certificate of Designations, will be validly issued, fully paid, and non-assessable.

The above opinions are expressed as of the date hereof, and we disclaim any undertaking to advise you of any subsequent changes to the facts stated or assumed herein and subsequent changes in applicable laws.

We hereby consent to the filing of this opinion letter with the Commission as Exhibit 5.1 to the Registration Statement and to the reference to our firm under the caption “Legal Matters” in the prospectus that forms a part of the Registration Statement. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.