EX-5.1

We are acting as counsel to Perspective Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with its automatic shelf registration statement on Form S‑3 (File No. 333-279692) (the “Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), relating to the registered offering of (i) 51,515,880 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”) to purchase an aggregate of 1,464,252 shares of Common Stock with an exercise price equal to $0.001 per share (the “Warrant Shares” and collectively with the Shares and the Warrants, the “Securities”). All of the Securities are to be sold by the Company pursuant to the Underwriting Agreement, dated as of May 24, 2024, between the Company and the representative of the several underwriters named therein (the “Underwriting Agreement”), as described in the prospectus, dated May 24, 2024 (the “Base Prospectus”), which forms a part of the Registration Statement, as supplemented by the Final Prospectus Supplement, dated May 24, 2024 (the “Final Prospectus Supplement” and, 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.

Hogan Lovells US LLP is a limited liability partnership registered in the state of Delaware. “Hogan Lovells” is an international legal practice that includes Hogan Lovells US LLP and Hogan Lovells International LLP, with offices in: Alicante Amsterdam Baltimore Beijing Berlin Birmingham Boston Brussels Colorado Springs Denver Dubai Dusseldorf Frankfurt Hamburg Hanoi Ho Chi Minh City Hong Kong Houston Johannesburg London Los Angeles Luxembourg Madrid Mexico City Miami Milan Minneapolis Monterrey Munich New York Northern Virginia Paris Philadelphia Rome San Francisco São Paulo Shanghai Silicon Valley Singapore Sydney Tokyo Warsaw Washington, D.C. Associated Offices: Budapest Jakarta Riyadh Shanghai FTZ Ulaanbaatar. Business Service Centers: Johannesburg Louisville. Legal Services Center: Berlin. For more information see www.hoganlovells.com

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:

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 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.