Exhibit 5.1

Our Reference: CM/LI225/063

1 July 2026

PRIVATE AND CONFIDENTIAL

Board of Directors

SMX (Security Matters) Public Limited Company

Mespil Business Centre

Mespil House

Sussex Road

Dublin 4

Ireland

D04 T4A6

Re:

SMX (Security Matters) Public Limited Company

To whom it may concern,

1.	Basis of Opinion (the “Opinion”)

1.1

We have acted as solicitors in Ireland to SMX (Security Matters) Public Limited Company, a public company limited by shares incorporated under the laws of Ireland under company registration number 722009 (the “Company”), in connection with the proposed issuance and sale by the Company of up to an aggregate of 25,414,300 ordinary shares in the capital of the Company of US$0.00000000558603475 par value per share (“Shares”) that the Selling Stockholders (as defined in the Registration Statement) may receive pursuant to Shares that the Company may, in its discretion, elect to issue and sell to the one of the Selling Stockholders, from time to time after the date of the Registration Statement, pursuant to that certain Standby Equity Purchase Agreement, dated 1 December 2025, between the Company and the SEPA Investor (the “SEPA”), as amended by the Amendment and Addendum to the SEPA dated 9 December 2025 (the “First SEPA Amendment”), and as further amended by the Second Amendment to the SEPA dated 6 February 2026 (the “Second SEPA Amendment”) in which the SEPA Investor has committed to purchase from the Company up to US$250,000,000 of the Company’s Shares in an equity line of credit, subject to the terms and conditions specified in the SEPA.

	1.2	We refer to the registration statement on Form F-3 to be filed by the Company with the U.S. Securities and Exchange Commission pursuant to the Securities Act of 1933, as amended (the “Securities Act”), as amended from time to time (the “Registration Statement”), and the transactions contemplated therein (the “Transaction”).

	1.3	Terms used but not defined herein shall have the meaning assigned to them in the Registration Statement.

	1.4	This Opinion is solely for the benefit of the addressees of this Opinion and may not be relied upon, used, transmitted, referred to, quoted from, circulated, copied, filed with any governmental agency or authority, disseminated or disclosed by or to any other person or entity for any purpose(s) without our prior written consent.

	1.5	This Opinion is given on the basis that our client is the Company. For the purposes of giving this Opinion, we have taken instructions solely from our client.

	1.6	This Opinion is strictly confined to:

	(a)	the matters expressly stated herein and is not to read as extending by implication or otherwise to any other matter;

	(b)	the Transaction; and

	(c)	the searches listed in paragraph 1.12 below (the “Searches”) (and no other searches whatsoever),

and is subject to the assumptions and qualifications set out below.

	1.7	We express no opinion and make no representation or warranty, as to any matter of fact or in respect of any documents which may exist in relation to the Transaction other than the Transaction Documents.

	1.8	In giving this Opinion, we have relied upon the Searches and we give this Opinion expressly on the terms that no further investigation or diligence in respect of any matter referred to in the Searches is required of us.

	1.9	For the purposes of this Opinion, we have reviewed the following documents (collectively, the “Documents”):

	(a)	the constitution of the Company as at the date of this Opinion (the “Constitution”);

	(b)	Certificate of Incorporation of the Company on registration as a public limited company dated 1 July 2022;

	(c)	Certificate of Incorporation on Change of Name of the Company dated 17 February 2023;

	(d)	a corporate certificate delivered by a director of the Company on or about the date hereof (the “Officer’s Certificate”);

	(e)	the Searches;

	(f)	a draft of the Registration Statement sent to us by Ruskin Moscou Faltischek, P.C. by email on 1 July 2026;

	(g)	a copy of signed minutes of a meeting of the board of directors of the Company (the “Board”) dated 5 February 2026 and 19 March 2026;

	(h)	the SEPA;

	(i)	the First SEPA Amendment; and

	(j)	the Second SEPA Amendment,

(references in this Opinion to the “Transaction Documents” are to items (h) through (j) above).

	1.10	This Opinion is confined to and given in all respects on the basis of the laws of Ireland (meaning Ireland exclusive of Northern Ireland) in force as at the date of this Opinion as currently applied by the courts of Ireland and, in relation to the opinion on taxation set out in paragraph 2.4, is given also on the basis of our understanding of the practices of the Irish Revenue Commissioners on the date hereof. We have made no investigations of, and we express no opinion as to the laws of, any other jurisdiction or their effect on this Opinion. This Opinion speaks only as of its date. We assume no obligation to update this Opinion at any time in the future or to advise you of any change in law, change in interpretation of law or change in the practice of the Irish Revenue Commissioners, which may occur after the date of this Opinion.

	1.11	In giving this Opinion, we have examined copies of the Documents sent to us by email in pdf or other electronic format.

	1.12	For the purpose of giving this Opinion, we have caused to be made the following legal searches against the Company on 1 July 2026 (the “Searches”):

	(a)	on the file of the Company maintained by the Registrar of Companies in Dublin for mortgages, debentures or similar charges or notices thereof and for the appointment of any receiver, examiner or liquidator;

	(b)	in the Judgments Office of the Irish High Court for unsatisfied judgments, orders, decrees and the like for the five years immediately preceding the date of the search; and

	(c)	in the Central Office of the Irish High Court in Dublin for any proceedings and petitions filed in the last two years.

	1.13	This Opinion is governed by and is to be construed in accordance with the laws of Ireland as interpreted by the courts of Ireland at the date of this Opinion.

	1.14	No opinion is expressed as to the taxation consequences of the Transaction or the transactions contemplated thereby.

	1.15	The opinion set out in paragraph 2.4 represents only our interpretation of Irish tax laws and has no binding, legal effect on, without limitation, the Irish Revenue Commissioners or any court. It is possible that contrary positions may be asserted by the Irish Revenue Commissioners and that one or more courts may sustain such contrary positions. The authorities upon which we rely may change at any time, potentially with retroactive effect. No assurances can be given as to the effect of any such changes on the conclusions expressed in paragraph 2.4.

2.	Opinion

Subject to the assumptions set out in this Opinion and to any matters not disclosed to us, we are of the opinion that:

	2.1	the Company is a public limited company, is duly incorporated and validly existing under the laws of Ireland and has the requisite corporate authority to issue the Shares;

	2.2	the Shares, when issued and allotted by the Company in accordance with the terms of the Transaction Documents, will have been duly authorised pursuant to resolutions of the Board or a duly appointed committee thereof;

	2.3	upon the issuance and allotment of the Shares in accordance with (a) all necessary corporate action of the Company; and (b) the Transaction Documents, the Shares will be validly issued, fully paid or credited as fully paid and non-assessable (which term means that no further sums are required to be paid by the holders thereof in connection with the issue of the Shares);

	2.4	subject to the foregoing and the qualifications and limitations set forth in the Registration Statement, the discussion of the Irish tax consequences described in the Registration Statement under the heading “Certain Material Irish Tax Considerations To Non-Irish Holders”, to the extent that it describes Irish tax laws or legal conclusions with respect thereto, is an accurate summary of the tax consequences described therein in all material respects and such statements constitute our opinion.

3.	Assumptions

For the purpose of giving this Opinion we assume the following, without any responsibility on our part if any assumption proves to have been untrue as we have not verified independently any assumption:

Registration Statement and the Shares

	3.1	that, when filed with the SEC, the Registration Statement will not differ in any material respect from the final draft that we have examined and that before any Shares are offered, issued and sold, the Registration Statement and any amendments to the Registration Statement (including post-effective amendments) will have become effective under the Securities Act;

	3.2	that the filing of the Registration Statement with the SEC has been authorised by all necessary actions under all applicable laws other than Irish law;

	3.3	that any Shares issued under the Transaction Documents will be in consideration of the receipt by the Company prior to the issuance of such Shares pursuant thereto of either cash or the release of a liability of the Company for a liquidated sum, at least equal to the nominal value of such Shares and any premium required to be paid up on the Shares pursuant to their terms of issuance;

	3.4	that, with respect to Shares allotted and issued after the date of expiry of the Company’s existing authority to allot and issue securities, that the Company will have renewed its authority to allot and issue the Shares and dis-apply the statutory pre-emption rights in accordance with the requirements of the Constitution and the Companies Act for the remainder of the period that the Registration Statement will continue in effect, and that, where such authorities have not been renewed, the Company will not allot and issue the Shares after such authorities have expired;

	3.5	that, at the time of any issuance of any Shares, the Company validly exists under the laws of Ireland and has the necessary corporate power and authority to issue such Shares under the terms of the Transaction Documents;

	3.6	that any issuance and allotment of Shares will be in compliance with the Companies Act, the Irish Takeover Panel Act 1997, Takeover Rules 2022, and all applicable Irish company, takeover, securities, market abuse, insider dealing laws and other rules and regulations;

	3.7	that all Shares issued and allotted under the Transaction Documents will be issued and sold in compliance with all applicable laws (other than Irish law), including applicable U.S. federal and state securities law, and in accordance with the Transaction Documents;

	3.8	that the execution and delivery by the Company of, and the performance of its obligations under the Transaction Documents, will not violate, conflict with or constitute a default under:

	(a)	the Constitution;

	(b)	any agreement, instrument, undertaking, arrangement, deed or covenant affecting the Company or its properties or to which the Company is a party or otherwise bound or subject;

	(c)	any law, rule or regulation to which the Company or its properties is subject;

	(d)	any judicial or regulatory order or decree of any governmental authority; or

	(e)	any consent, approval, license, authorisation or validation of, or filing, recording or registration with, any governmental authority;

	3.9	that the Selling Stockholders will pay in full all amounts that they have agreed to subscribe for the Shares;

	3.10	that the Registration Statement does not constitute (and is not intended/required to constitute) a prospectus within the meaning of Part 23 of the Companies Act and to the extent that any offer of Shares is being made to investors in any member state of the European Union, the Company is satisfied that the obligation to propose and publish a prospectus pursuant to Irish prospectus law, or in particular pursuant to the European Union (Prospectus) Regulations 2019, does not arise;

	3.11	there shall be no fraud on the part of the Company and its respective officers, employees, agents and advisers and that the Company will effect the issuance of the Shares in good faith, for its legitimate and bona fide business purposes;

	3.12	that (i) the Shares will be quoted on the Nasdaq Capital Market of the Nasdaq Stock Market LLC at the time of the issuance of the Shares and will continue to be so quoted or (ii) the Shares will not derive their value or the greater part of their value directly or indirectly from land in Ireland, minerals in Ireland or any rights, interests or other assets in relation to mining or minerals or the searching for minerals or exploration or exploitation rights on the Irish continental shelf;

Authenticity and bona fides

	3.13	the truth, completeness, accuracy and authenticity of all Documents submitted to us as originals or copies of originals (and in the case of copies, conformity to the originals of such copies), the genuineness of all signatories, stamps and seals thereon and where incomplete Documents have been submitted to us that the originals of such Documents are identical to the last draft of the complete Documents submitted to us;

	3.14	that the copies produced to us of minutes of meetings and/or of resolutions correctly record the proceedings at such meetings and/or the subject matter which they purport to record and that any meetings referred to in such copies were duly convened, duly quorate and held, that those present at any such meetings were entitled to attend and vote at the meeting and acted bona fide throughout and that no further resolutions have been passed or other action taken which would or might alter the effectiveness thereof and that such resolutions have not been amended or rescinded and are in full force and effect;

	3.15	that there is, at the relevant time of the allotment and issuance of the Shares, no matter affecting the authority of the directors to allot and issue the Shares, not disclosed by the Constitution or the resolutions produced to us, which would have any adverse implications in relation to the opinions expressed in this Opinion;

	3.16	that each director of the Company has disclosed any interest which he or she may have in the Transaction in accordance with the provisions of the Companies Act and the Constitution and none of the directors of the Company has any interest in the Transaction except to the extent permitted by the Constitution;

	3.17	the absence of fraud, coercion, duress or undue influence and lack of bad faith on the part of the Company and its respective officers, employees, agents and advisers and that the Company will issue the Shares in good faith, for its legitimate and bona fide business purposes;

	3.18	that the representations contained in the Officer’s Certificate are correct as to questions of fact;

	3.19	that the persons identified as the directors of the Company are actually serving as such and that any certificates representing the Shares will be properly executed by one or more such persons;

Constitution, Agreements and Resolutions

	3.20	that the Constitution included in the Officer’s Certificate is the current constitution of the Company and that there were no other terms governing the Shares other than those set out in the Constitution and the Documents (as applicable);

	3.21	all director and shareholder resolutions required to authorise the issuance of the Shares have been validly passed prior to the issuance of the Shares, and shall not have been revoked, rescinded or amended;

Solvency and Insolvency

3.22

that (i) the parties to the Transaction Documents were solvent and able to pay their debts within the meaning of section 570 of the Companies Act or any analogous provisions under any applicable laws immediately after the execution and delivery of the Transaction Documents; (ii) the parties to the Transaction Documents will not as a consequence of doing any act or thing which the Transaction Documents contemplate, permit or require the relevant party to do, be unable to pay its debts within the meaning of section 570 of the Companies Act or any analogous provisions under any applicable laws; (iii) no liquidator, receiver or examiner or other similar or analogous officer has been appointed in relation to any of the assets or undertakings of the parties to the Transaction Documents; and (iv) no petition for the making of a winding-up order or the appointment of an examiner or any similar officer or any similar or analogous procedure in any jurisdiction has been presented in relation to the parties to the Transaction Documents;

Accuracy of Searches and Warranties

	3.23	the accuracy and completeness of the information disclosed in the Searches referred to in paragraph 1.11 above and that such information has not since the time of such search or enquiry been altered (it should be noted that searches at the Companies Registration Office, Dublin, do not necessarily reveal whether or not a prior charge has been created or a resolution has been passed or a petition presented or any other action taken for the winding-up of or the appointment of a receiver or an examiner to the Company);

	3.24	the truth, completeness and accuracy of all representations and statements as to factual matters contained in the Documents.

Commercial Benefit

3.25

that the Transaction Documents have been entered into for bona fide commercial purposes, on arm’s length terms and for the benefit of each party thereto and are in those parties’ respective commercial interests and for their respective corporate benefit;

Financial Assistance and Connected Transactions

	3.26	that the Company is not, by entering into the Transaction Documents or performing its obligations thereunder, providing financial assistance for the purpose of an acquisition (by way of subscription, purchase, exchange or otherwise) made or to be made by any person of any shares in the Company which would be prohibited by section 82 of the Companies Act; and

	3.27	that none of the transactions contemplated by the Transaction Documents are prohibited by virtue of section 239 of the Companies Act, which prohibits certain transactions between companies and its directors or persons connected with its directors.

Governing Law and Jurisdiction

3.28

that under all applicable laws (other than those of Ireland):

	(a)	the choice of the laws of the State of Arizona as the governing law of the Transaction Documents (to the extent that they are expressed to be governed by the laws of the State of Arizona) is a valid and binding selection which will be upheld, recognised and given effect by the courts of any relevant jurisdiction (other than those of Ireland); and

	(b)	the submission of each party to the Transaction Documents to the exclusive jurisdiction of the state and federal courts sitting in Maricopa County, Arizona (to the extent that they are so expressed) is valid and binding and will be upheld, recognised and given effect by the courts of any relevant jurisdiction (other than those of Ireland).

4.	Qualifications

The opinions set out in this Opinion are subject to the following reservations:

General Matters

	4.1	A particular course of dealing among the parties or an oral amendment, variation or waiver may result in an Irish court finding that the terms of the Transaction Documents have been amended, varied or waived even if such course of dealing or oral amendment, variation or waiver is not reflected in writing among the parties.

	4.2	No opinion is expressed on the irrevocability of, or on the enforceability of the delegation of, any power of attorney under the Transaction Documents.

	4.3	No opinion is expressed on any deed of assignment, transfer, accession or similar document executed after the date of this opinion in relation to any of the rights and obligations contained in the Transaction Documents.

	4.4	No opinion is expressed on any deed or agreement envisaged by the Transaction Documents to be entered at a future date or any future action taken by a party under the Transaction Documents.

	4.5	We express no opinion as to whether the Transaction Documents breach any other agreement or instrument.

Sanctions

4.6

If any party to the Transaction Documents or to any transfer of, or payment in respect of, the Transaction Documents is controlled by or otherwise connected with a person (or is itself) resident in, incorporated in or constituted under the laws of a country which is the subject of United Nations, European Union or Irish sanctions or sanctions under the Treaty on the Functioning of the European Union, as amended, or is otherwise the target of any such sanctions, then obligations to that party under the Transaction Documents or in respect of the relevant transfer or payment may be unenforceable or void.

5.	Disclosure

This Opinion is addressed to you in connection with the registration of the Shares with the SEC. We hereby consent to the inclusion of this Opinion as an exhibit to the Registration Statement to be filed with the SEC and to the use of our name in the proxy statement/prospectus that forms part of the Registration Statement.

6.	No Refresher

This Opinion speaks only as of its date. We are not under any obligation to update this Opinion from time to time or to notify you of any change of law, fact or circumstances referred to or relied upon in the giving of this Opinion.

This Opinion is governed by and is to be construed in accordance with the laws of Ireland as interpreted by the courts of Ireland at the date hereof.

Yours faithfully,


ARTHUR COX LLP