Exhibit 5.1

April 21, 2026

CDT Equity Inc.

4851 Tamiami Trail North, Suite 200

Naples, FL 34103

Ladies and Gentlemen:

We have acted as counsel for CDT Equity Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing of a Registration Statement on Form S-3 (the “Registration Statement”), including a related preliminary prospectus filed with the Registration Statement (the “Prospectus”), with the U.S. Securities and Exchange Commission (the “Commission”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), covering the offer and sale by the selling stockholders identified therein of up to 5,348,058 shares of the Company’s common stock, par value $0.0001 per share (the “Common Stock”) comprised of (i) up to 925,925 shares of Common Stock (“ELOC Shares”) issued pursuant to an amendment entered into on March 3, 2026 (the “Amendment”) to the directed stock purchase agreement entered into on January 16, 2026 (the “ELOC Purchase Agreement”) by and between the Company and Ascent Partners Fund LLC relating to an equity line of credit; and (ii) 4,422,133 shares of Common Stock (the “Sarborg Shares,” and together with the ELOC Shares, the “Shares”) issued pursuant to the Securities Purchase Agreement entered into on February 19, 2026 (the “Purchase Agreement”), by and between the Company and all the stockholders of Sarborg Limited (“Sarborg”).

In connection with this opinion, we have examined originals or copies (certified or otherwise identified to our satisfaction) of (i) the Company’s Certificate of Incorporation as amended and/or restated to date and as currently in effect (the “Certificate of Incorporation”), (ii) the Company’s Bylaws as amended and/or restated to date and as currently in effect (the “Bylaws”), (iii) the Registration Statement and the Prospectus, (iv) the Amendment, ELOC Purchase Agreement, and Purchase Agreement, and (v) such corporate records, agreements, documents, and other instruments, and such certificates or comparable documents of public officials or of officers and representatives of the Company, as we have deemed relevant and necessary as a basis for the opinion hereinafter set forth.

In such examination, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed or photostatic copies, the authenticity of the originals of such latter documents, that all parties (other than the Company) had the requisite power and authority (corporate or otherwise) to execute, deliver, and perform such agreements or instruments, that all such agreements or instruments have been duly authorized by all requisite action (corporate or otherwise), executed and delivered by such parties, and that such agreements or instruments are valid, binding, and enforceable obligations of such parties. As to certain questions of fact material to this opinion letter, we have relied upon certificates or comparable documents of officers and representatives of the Company and have not sought to independently verify such facts.

Based on the foregoing, and subject to the assumptions, limitations and qualifications stated herein, we are of the opinion that the Shares have been duly authorized and, when issued pursuant to each of the Amendment, ELOC Purchase Agreement, and Purchase Agreement, respectively, will be validly issued, fully paid, and non-assessable.

300 Madison Avenue, 27th Floor New York, New York 10017

www.ThompsonHine.com O: 212.344.5680 F: 212.344.6101

In rendering the foregoing opinion, we have assumed that, (i) before the Shares are issued, the Company will not issue shares of Common Stock or reduce the total number of shares of Common Stock that the Company is authorized to issue under its then-effective Certificate of Incorporation such that the number of unissued shares of Common Stock authorized under the Certificate of Incorporation is less than the aggregate number of Shares, (ii) the Company will comply with all applicable notice requirements regarding uncertificated shares provided in the DGCL (as defined below), and (iii) upon the issuance of any of the Shares, the total number of shares of Common Stock issued and outstanding will not exceed the total number of shares of Common Stock that the Company is then authorized to issue under its Certificate of Incorporation.

Notwithstanding the foregoing, for purposes of rendering the opinion set forth above with respect to the ELOC Shares, we have further assumed (i) the approval by the Company’s board of directors (the “Board of Directors”) (or duly authorized designees of the Board of Directors) of each issuance of the ELOC Shares, (ii) the issuance of the ELOC Shares in accordance with such approval, for a price per share equal to or greater than the minimum price, if any, authorized by the Board of Directors (or duly authorized designees of the Board of Directors) prior to the date of issuance (the “Minimum Price”), (iii) the receipt by the Company of the consideration (which shall not be less than the par value of such ELOC Shares) to be paid in accordance with such approval, and (iv) that no event occurs that causes the total number of ELOC Shares that may be issued for the Minimum Price, when added to the number of shares of the Common Stock issued, subscribed for, or otherwise committed to be issued, to exceed the number of authorized shares of the Common Stock available for issuance by the Company.

The opinion expressed herein is limited to the General Corporation Law of the State of Delaware (including reported judicial decisions interpreting the General Corporation Law of the State of Delaware) (the “DGCL”) and we express no opinion as to the effect on the matters covered by this opinion of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference to our firm under the caption “Legal Matters” in the Prospectus. In giving such consents, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,