Exhibit 5.1

Hogan Lovells US LLP 609 Main Street, Suite 4200 Houston, TX 77002 T +1 713 632 1400 F +1 713 632 1401 www.hoganlovells.com

January 22, 2024

Board of Directors         

Perspective Therapeutics, Inc.

2401 Elliott Avenue, Suite 320

Seattle, Washington 98121

Ladies and Gentlemen:

We are acting as counsel to Perspective Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with its registration statement on Form S‑3, as amended (File No. 333-275638) (the “Registration Statement”), filed with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Act”), relating to the public offering of up to (i) 156,399,542 shares of common stock, par value $0.001 per share (the “Common Stock”) of the Company (the “Shares”) and (ii) pre-funded warrants (the “Warrants” and, together with the Shares, the “Securities”) to purchase an aggregate of 30,086,944 shares of Common Stock with an exercise price equal to $0.001 per share (the “Warrant Shares”). All of the Securities are to be sold by the Company pursuant to the Underwriting Agreement, dated as of January 17, 2024, between the Company and the representative of the several underwriters named therein (the “Underwriting Agreement”), as described in the prospectus, dated December 14, 2023 (the “Base Prospectus”), which forms a part of the Registration Statement, as supplemented by the Prospectus Supplement, dated January 17, 2024 (the “Prospectus Supplement”, together with the Base Prospectus, the “Prospectus”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S‑K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinions hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including pdfs). As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

This opinion letter is based as to matters of law solely on the Delaware General Corporation Law, as amended. We express no opinion herein as to any other statutes, rules or regulations.

Based upon, subject to and limited by the foregoing, we are of the opinion that:

1. Following (i) issuance of the Shares pursuant to the terms of the Underwriting Agreement and (ii) receipt by the Company of the consideration for the Shares specified in the resolutions of the Board of Directors or the Pricing Committee of the Board of Directors, the Shares will be validly issued, fully paid and nonassessable.

2. Following (i) execution and delivery by the Company of the Warrants pursuant to the terms of the Underwriting Agreement and (ii) receipt by the Company of the consideration for the Warrants specified in the resolutions of the Board of Directors or the Pricing Committee of the Board of Directors, the Warrants will constitute valid and binding obligations of the Company.

3. The Warrant Shares have been duly authorized and, when issued, delivered and paid for upon exercise in accordance with the provisions of the Warrants, will be validly issued, fully paid, and nonassessable.

This opinion letter has been prepared for use in connection with the Registration Statement. We assume no obligation to advise of any changes in the foregoing subsequent to the effective date of the Registration Statement.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Company’s Current Report on Form 8-K to be filed with the Securities and Exchange Commission on the date hereof and to the reference to this firm under the caption “Legal Matters” in the Prospectus constituting a part of the Registration Statement. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Act.

Very truly yours,

/s/ HOGAN LOVELLS US LLP

HOGAN LOVELLS US LLP