EXHIBIT 5.1

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Trinity Biotech plc IDA Business Park Bray County Wicklow Ireland



Our ref		13 May 2026
4031/2 DJ/TB/LC

Dear Addressee

Registration Statement on Form F-3 of Trinity Biotech plc

Registration, Offer and Resale of American Depositary Shares

1 Introduction

We act as legal advisers to Trinity Biotech plc, a public limited company incorporated under the laws of Ireland with company number 183476 (the “Company”), which has asked us to give this Opinion as to certain matters of Irish law in connection with the filing by the Company on the date hereof of a registration statement on Form F-3 (the “Registration Statement”) with the U.S. Securities and Exchange Commission (the “Commission”) under the U.S. Securities Act of 1933, as amended (the “Securities Act”).

The Registration Statement relates to the registration, offer and resale, from time to time, by the Selling Securityholder (as named therein) of up to 33,752,429 American Depositary Shares (the “New ADSs”), representing, in aggregate, up to 675,048,580 A Ordinary Shares of US$0.0001 each (nominal value) in the capital of the Company (“A Ordinary Shares”) to be allotted in connection therewith (such number of A Ordinary Shares being, the “New Shares”). Each New ADS represents 20 New Shares. The New Shares and the New ADSs are proposed to be allotted, issued and delivered pursuant to a New York law governed Standby Equity Purchase Agreement dated 24 February 2026 made by and among the Company and YA II PN, LTD (the “SEPA”).

The New Shares and the New ADSs are further proposed to be allotted, issued and delivered, as the case may be, pursuant to a New York law governed Deposit Agreement dated 21 October 1992, as amended and restated on 15 January 2004 made by and among the Company, The Bank of New York Mellon (the “Depositary”) and the owners and holders of American Depositary Receipts evidencing American Depositary Shares issued thereunder (the “Deposit Agreement” and together with the SEPA, the “Agreements”).

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The New Shares are proposed to be allotted and issued to, and registered in the name of BNY (Nominees) Limited (the “Custodian”), as agent and nominee of the Depositary under the Deposit Agreement.

2 Basis of Opinion

For the purpose of giving this Opinion, we have examined the documents and have conducted the searches listed in Schedule 1 (Documents and Searches) to this Opinion, together with such other materials as we have considered necessary or relevant as a basis for the opinions contained herein.

This Opinion is strictly limited to the matters expressly stated under Section 3 (Opinions), below, and is not to be read as extending, by implication or otherwise, to any other matter. In particular, this Opinion does not deal with any tax matter or the tax consequences of any matter referred to in this Opinion, in the documents or other materials examined by us for the purpose of giving this Opinion, or otherwise.

We express no opinion and make no representation or warranty as to any matter of fact. We have not investigated or verified any of the facts or assumptions, or the reasonableness of any assumptions, statements or opinions contained or represented by any person in the documents or other materials examined by us for the purposes of giving this Opinion, nor have we attempted to determine if any relevant facts have been omitted from such documents or materials.

This Opinion is given with respect to the laws of Ireland in effect on the date hereof and is based on legislation published and cases fully reported before that date and our knowledge of the facts relevant to the opinions contained herein. For the avoidance of doubt, Ireland does not include Northern Ireland (which is a separate jurisdiction), and references to the laws of Ireland do not include the laws in force in Northern Ireland.

We have made no investigations of, and we express no opinion on, the laws of any jurisdiction other than Ireland, or the effect thereof. In particular, we have made no investigations of any reference to non-Irish laws in any document or other materials examined by us or the meaning of effect thereof, and any phrases used in any non-Irish law governed document examined by us have been construed by us as having the meaning and effect they would have if such document was governed by Irish law. We have assumed, without enquiry, that there is nothing in the laws of any jurisdiction other than Ireland which would, or might, affect the opinions contained herein, and that, insofar as the laws of any jurisdiction other than Ireland are relevant, such laws have been, or will be, complied with.

This Opinion is expressed as of the date hereof and we assume no obligation to update the opinions contained herein.

3 Opinions

Based upon, and subject to, the foregoing and the assumptions, qualifications and limitations set out in Schedule 2 (Assumptions), Schedule 3 (Qualifications) and elsewhere in this Opinion, we are of the following opinions:

(a) The Company is a public limited company, duly incorporated and validly existing under the laws of Ireland.

(b) The New Shares, when allotted and issued in accordance with the terms and conditions of the SEPA against receipt by the Company of the full consideration payable therefor, will, upon the entry of the name(s) of the Custodian or other relevant allottee(s) in the register of members of the Company as the registered holder(s) thereof (in each case credited as fully paid-up) be validly issued, fully paid-up and non-assessable. “Non-assessable” is a phrase which has no defined meaning under Irish law, but, for the purposes of this Opinion, shall mean a registered holder of such New Shares is not subject, solely by virtue of its shareholding, to calls for additional payments of capital on such shares. As a matter of Irish law, a share in an Irish incorporated company is only issued when it has been entered in the register of members of the relevant company.

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4 Reliance

This Opinion is furnished to you and the persons entitled to rely upon it pursuant to the applicable provisions of the Securities Act strictly for use in connection with the Registration Statement and may not be relied upon by any other person without our prior written consent.

5 Consent

We hereby consent to the filing of this Opinion as Exhibit 5.1 to the Registration Statement and to the reference to Matheson LLP under the caption “Legal Matters” in the prospectus forming part of the Registration Statement. In giving such consent, we do not admit that we are included in the category of persons whose consent is required under section 7 of the Securities Act, or the rules and regulations of the Commission promulgated thereunder.

6 Governing Law

This Opinion and the opinions contained herein are governed by, and construed in accordance with, the laws of Ireland.

Yours faithfully

/s/ Matheson LLP

MATHESON LLP

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Schedule 1

Documents and Searches

For the purposes of giving this Opinion, we have examined the documents and have conducted the searches listed below.

1. The final form of the Registration Statement to which this Opinion is to be filed as an exhibit.

2. A .pdf copy of the SEPA.

3. A .pdf copy of the Deposit Agreement.

4. A certificate issued by the secretary of the Company dated the date of this Opinion (the “Corporate Certificate”):

(a) attaching a copy of each of the following documents certified as being true, complete and correct by the secretary:

(i) the Company’s certificate of incorporation dated 22 January 1992, certificate of incorporation on change of name dated 24 February 1992, certificate of incorporation on change of name dated 16 July 1992 and certificate of incorporation on re-registration as a public limited company dated 16 July 1992 (the “Certificates of Incorporation”);

(ii) the memorandum of association of the Company as amended on 30 September 2025 (the “Memorandum of Association”) and the articles of association of the Company adopted on 30 September 2025 (the “Articles of Association”, and together with the Certificates of Incorporation and the Memorandum of Association, the “Constitutional Documents”);

(iii) written resolutions of all the directors of the Company passed on 24 February 2026 (the “Written Board Resolutions”);

(iv) the minutes of the 2025 annual general meeting of the Company held on 30 September 2025 (the “AGM Minutes”); and

(b) certifying certain other matters, as set out therein, on which we have relied for the purpose of this Opinion.

5. Searches carried out by independent law researchers on our behalf against the Company on 13 May 2026: (a) in the Register of Winding-up Petitions maintained at the Central Office of the High Court of Ireland; (b) in the Judgments’ Office of the High Court of Ireland; and (c) on the file of the Company maintained by the Registrar of Companies at the Irish Companies Registration Office (the “Companies Registration Office”) (the “Searches”).

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Schedule 2

Assumptions

The opinions contained herein are given on the basis of the assumptions set out in this Schedule.

1. All signatures (including, for the avoidance of doubt, electronic signatures), initials, seals and stamps contained in, or on, any document examined by us are genuine.

2. All documents provided to us as originals are authentic and complete and all documents provided to us as copies (including, without limitation, any document provided to us as a .pdf (or any other format) attachment to an email) are complete and conform to the originals of such documents, and the originals of such documents are authentic and complete with all requisite seals and stamps affixed.

3. The contents of the documents and any other materials examined by us for the purposes of this Opinion are true and accurate as to factual matters, but we have made no independent investigation regarding such factual matters.

4. All documents dated on, or prior to, the date hereof and on which we have expressed reliance have not been revoked or amended and remain accurate.

5. Each natural person who has executed any document examined by us for the purposes of this Opinion had the due personal legal capacity to do so.

6. Any electronic signature inserted on a document was inserted by the signatory in question and not by another person and where attested by a witness was inserted in the physical presence of the witness. Each party to any document which has been executed using electronic signatures has consented to the execution of that document by way of electronic signature.

7. The SEPA has been delivered by the parties thereto (including the Company) and is not subject to any escrow or similar arrangement, and the transactions provided for in the SEPA will be consummated upon the terms and conditions provided for therein.

8. There have been no amendments to the Constitutional Documents or the other attachments to the Corporate Certificate.

9. The Written Board Resolutions have not, since their date of adoption, been amended, superseded or rescinded, and are in full force and effect.

10. The members’ resolutions documented in the AGM Minutes were passed at a properly convened, constituted and quorate meeting of the members of the Company, and such resolutions have not, since their date of adoption, been amended, superseded or rescinded, and are in full force and effect.

11. The Company will derive a commercial benefit from entering into the SEPA commensurate with the obligations undertaken by it thereunder.

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12. In approving the entry into the SEPA and the allotment, issue and delivery of the New Shares and New ADSs upon the terms and conditions provided for therein, the directors of the Company have acted in good faith in the interests of the Company for the benefit of its members as a whole and for its legitimate business purposes.

13. The Company will have received the full consideration payable for any New Shares (as provided for in the SEPA) prior to, or simultaneous with, their allotment and issue, and no New Share shall be allotted and issued for consideration that is less than its nominal value.

14. At the time of the allotment and issue of any New Shares, the Company will continue to have a sufficient number of unissued A Ordinary Shares in its authorised share capital, being at least equal to the number of New Shares to be allotted and issued, and the Company shall not take any action that would reduce the number of unissued A Ordinary Shares below such amount.

15. Each person to whom New Shares are allotted and issued under the SEPA will have the due and requisite capacity (and, if relevant, will have taken all necessary corporate actions to be authorised) to be allotted and issued New Shares and to be registered in the register of members of the Company as the holder thereof. Each such person has agreed to become a member of the Company.

16. The information disclosed by the Searches was accurate and complete as of the date the Searches were made and has not been altered, the Searches did not fail to disclose any information which had been delivered for registration but which did not appear from the information available at the time the Searches were made or which ought to have been delivered for registration at that time but had not been so delivered and no additional matters would have been disclosed by additional searches being carried out since that time.

17. At the time of the allotment and issue of any New Shares, the Company will not have passed a voluntary winding-up resolution or a resolution to place the Company under court protection or to appoint a process adviser, and no petition will have been presented to, or order will have been made by, a court for the winding-up of the Company or to place the Company under court protection or for the appointment of a process adviser.

18. The obligations expressed to be assumed by each party to the Agreements, all relevant documents referred to therein and all other documents examined by us for the purpose of this Opinion are legal, valid, binding and enforceable obligations under all applicable laws and in all applicable jurisdictions, other than, in the case of the obligations expressed to be assumed by the Company in the SEPA, the laws of Ireland and the jurisdiction of Ireland.

19. The Agreements and the transactions contemplated thereby and transfers and payments to be made thereunder are not and will not be affected or prohibited by any financial restrictions or sanctions imposed by the United Nations, the European Union or Ireland or which arise under any human rights, anti-terrorism, anti-corruption, anti-money laundering or exchange control laws and regulations of the European Union or Ireland, including, without limitation, any arising from orders made under the Financial Transfers Act 1992 of Ireland, the Criminal Justice (Terrorist Offences) Acts 2005 and 2015 of Ireland or the Criminal Justice (Money Laundering and Terrorist Financing) Acts 2010 to 2021 of Ireland.

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Schedule 3

Qualifications

The opinions contained herein are given subject to the qualifications set out in this Schedule.

1. A search in the Companies Registration Office will not reveal whether a petition has been presented to the Irish courts for the appointment of a liquidator or an examiner.

2. A search of the Register of Winding-up Petitions should reveal the existence of a petition for the appointment of a liquidator or an examiner but there may be a time lag between presentation and entry of particulars of the petition on the Register of Winding-up Petitions and accordingly a search of the Register of Winding-up Petitions may fail to reveal that any such petition has been presented. Furthermore in the case of certain smaller companies a petition for the appointment of an examiner may be presented to the Circuit Court and a search of the Register of Winding-up Petitions will not reveal the existence of such a petition.

3. A search in the Companies Registration Office should reveal the appointment of a liquidator, examiner, process adviser or receiver (whether by the Irish courts or, in the case of a liquidator, process adviser or a receiver, out of court). However, similarly there may be a time lag between the appointment and the filing of particulars of the appointment and accordingly a search in the Companies Registration Office may fail to reveal any such appointment.