Exhibit 5.1

777 East Wisconsin Avenue Milwaukee, WI 53202-5306 414.271.2400 TEL 414.297.4900 FAX foley.com   WRITER’S DIRECT LINE 414.297.5596 pfetzer@foley.com

January 26, 2026

Via E-Mail

Daxor Corporation

109 Meco Lane

Oak Ridge, TN 37830

Ladies and Gentlemen:

We have acted as counsel to Daxor Corporation, a New York corporation (the “Company”), in connection with the issuance and sale by the Company of up to 765,958 shares (the “Shares”) of common stock, par value $0.01 per share, of the Company (the “Common Stock”), pursuant to the Securities Purchase Agreement, dated January 23, 2026 (the “Purchase Agreement”), between the Company and the investors named therein.

This opinion letter is being furnished in accordance with the requirements of sub-paragraph (l) of item 25.2 of part C of Form N-2 under the Securities Act of 1933, as amended (the “Securities Act”), and the Investment Company Act of 1940, as amended (the “1940 Act”).

In rendering the opinions stated herein, we have examined and relied upon the following:

AUSTIN | BOSTON | BRUSSELS | CHICAGO | DALLAS | DENVER | DETROIT | HOUSTON | JACKSONVILLE | LOS ANGELES MADISON | MEXICO CITY | MIAMI | MILWAUKEE | NEW YORK | ORLANDO | RALEIGH | SACRAMENTO | SALT LAKE CITY SAN DIEGO | SAN FRANCISCO | SILICON VALLEY | TALLAHASSEE | TAMPA | TOKYO | WASHINGTON, D.C.

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinions stated below.

In our examination, we have assumed the genuineness of all signatures, including electronic signatures, the legal capacity and competency 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 facsimile, electronic, certified or photocopied copies, and the authenticity of the originals of such copies. As to any facts relevant to the opinions stated herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials, including the facts and conclusions set forth in the Secretary’s Certificate.

We are giving this opinion only as attorneys licensed to practice law in the State of Wisconsin. Our opinion, as set forth herein, is based on the facts in existence and the laws in effect on the date hereof and is limited to the federal laws of the United States of America and the New York Business Corporation Law and reported judicial decisions interpreting that law. We express no opinion as to the applicability or effect of the law of any jurisdiction other than that of the United States of America and the New York Business Corporation Law, and we disclaim any opinion as to any statute, rule, regulation, ordinance, order or other promulgation of any regional or local governmental authority.

As used herein, “Organizational Documents” means the Certificate of Incorporation and the Bylaws attached to the Secretary’s Certificate.

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that the Shares have been duly authorized by all requisite corporate action on the part of the Company under the New York Business Corporation Law and, when the Shares are issued and sold in accordance with the provisions of the Purchase Agreement upon payment of the consideration therefor determined by the Board of Directors, the Shares will be validly issued and fully paid, and under the New York Business Corporation Law, the holders of the Shares will have no obligation to make further payments for the purchase of such Shares or contributions to the Company solely by reason of their ownership of such Shares.

In rendering the foregoing opinions we have assumed that, at all applicable times:

We hereby consent to the reference to our firm under the headings “Legal Matters” in the Prospectus forming part of the Registration Statement. We also hereby consent to the filing or incorporation by reference of this opinion letter as an exhibit to the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable laws.