EX-5.1

We are acting as counsel to Perspective Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with its filing on the date hereof of a Post-Effective Amendment No. 2 to the registration statement on Form S-3 filed by the Company on May 24, 2024 (File No. 333-279692) (as amended, the “Registration Statement”). The Company has provided us with two prospectuses that form a part of the Registration Statement: (A) a base prospectus (the “Base Prospectus”), which provides that it may be supplemented in the future by one or more prospectus supplements (each, a “Prospectus Supplement”); and (B) a sales agreement prospectus (the “ATM Agreement Prospectus”) relating to the offering, issuance and sale by the Company of up to a maximum aggregate offering price of $250,000,000 of shares of common stock of the Company, $0.001 par value per share (the “Common Stock”) that may be issued and sold under that certain Controlled Equity OfferingSM Sales Agreement (the “Sales Agreement”), dated as of August 13, 2024, among the Company, Cantor Fitzgerald & Co. and RBC Capital Markets, LLC (such agreement, the “ATM Agreement,” and such shares of Common Stock to be sold thereunder, the “ATM Shares”). 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.

The Registration Statement, including the Base Prospectus (as supplemented from time to time by one or more Prospectus Supplements) and the ATM Agreement Prospectus, provides for the registration of the offering and sale by the Company of up to $500,000,000 in aggregate amount of an indeterminate amount of: (i) debt securities (the “Debt Securities”); (ii) shares of preferred stock, $0.001 par value per share (the “Preferred Stock”); (iii) shares of Common Stock; (iv) warrants to purchase Debt Securities, Preferred Stock or Common Stock (the “Warrants”); (v) units consisting of a combination of two or more of Debt Securities, Preferred Stock, Common Stock or Warrants (the “Units” and, together with the Debt Securities, Preferred Stock, Common Stock and Warrants, the “Securities”); and (vi) the ATM Shares.

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 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

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.

For purposes of this opinion letter, we have assumed that (i) the issuance, sale, amount and terms of any Securities of the Company to be offered from time to time will have been duly authorized and established by proper action of the board of directors of the Company or a duly authorized committee of such board (“Board Action”) consistent with the procedures and terms described in the Registration Statement and in accordance with the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws and applicable Delaware corporate law, in a manner that does not violate any law, government or court-imposed order or restriction or agreement or instrument then binding on the Company or otherwise impair the legal or binding nature of the obligations represented by the applicable Securities; (ii) at the time of offer, issuance and sale of any Securities, the Registration Statement will be effective under the Securities Act of 1933, as amended (the “Act”), and no stop order suspending its effectiveness will have been issued and remain in effect; (iii) any Debt Securities will be issued pursuant to an indenture for Debt Securities substantially in the form of the indenture filed as Exhibit 4.3 to the Registration Statement, with items shown in such exhibit as subject to completion having been completed in a satisfactory manner; (iv) the indenture under which any Debt Securities are issued will be qualified under the Trust Indenture Act of 1939, as amended; (v) any Warrants will be issued under one or more warrant agreements, as applicable, each to be between the Company and a financial institution identified therein as a warrant agent; (vi) any Units will be issued under one or more unit agreements; (vii) prior to any issuance of Preferred Stock, an appropriate certificate of designation will be accepted for record by the Secretary of State of the State of Delaware; (viii) if being sold by the Company, the Securities will be delivered against payment of valid consideration therefor and in accordance with the terms of the applicable Board Action authorizing such sale and any applicable underwriting agreement or purchase agreement and as contemplated by the Registration Statement and/or the applicable prospectus supplement; and (ix) the Company will remain a Delaware corporation.

To the extent that the obligations of the Company with respect to the Securities may be dependent upon such matters, we assume for purposes of this opinion (i) that the other party under the indenture for any Debt Securities, under the warrant agreement for any Warrants, under the unit agreement for any Units, namely, the trustee, the warrant agent or the unit agent, respectively, is duly organized, validly existing and in good standing under the laws of its jurisdiction of organization; (ii) that such other party is duly qualified to engage in the activities contemplated by such indenture, warrant agreement, or unit agreement, as applicable; (iii) that such indenture, warrant agreement, or unit agreement, as applicable, has been duly authorized, executed and

delivered by the other party and constitutes the legal, valid and binding obligation of the other party enforceable against the other party in accordance with its terms; (iv) that such other party is in compliance with respect to performance of its obligations under such indenture, warrant agreement, or unit agreement, as applicable, with all applicable laws, rules and regulations; and (v) that such other party has the requisite organizational and legal power and authority to perform its obligations under such indenture, warrant agreement, or unit agreement, as applicable.

This opinion letter is based as to matters of law solely on the applicable provisions of the following, as currently in effect: (i) the Delaware General Corporation Law, as amended, and (ii) as to the opinions given in paragraphs (a), (d) and (e), the laws of the State of New York (but not including any laws, statutes, ordinances, administrative decisions, rules or regulations of any political subdivision below the state level). We express no opinion herein as to any other statutes, rules or regulations (and in particular, we express no opinion as to any effect that such other statutes, rules or regulations may have on the opinions expressed herein).

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

(a) The Debt Securities (including any Debt Securities duly issued upon the exercise of Warrants and receipt by the Company of any additional consideration payable upon such exercise), upon due execution and delivery of an indenture relating thereto on behalf of the Company and the trustee named therein, and upon authentication by such trustee and due execution and delivery on behalf of the Company in accordance with the indenture and any supplemental indenture relating thereto, will constitute valid and binding obligations of the Company.

(b) The Preferred Stock (including any Preferred Stock duly issued upon the exchange or conversion of Debt Securities that are exchangeable for or convertible into Preferred Stock or upon the exercise of Warrants and receipt by the Company of any additional consideration payable upon such conversion, exchange or exercise), upon due execution and delivery on behalf of the Company of certificates therefor, including global certificates, or the entry of the issuance thereof in the books and records of the Company, as the case may be, will be validly issued, fully paid and nonassessable.

(c) The Common Stock (including any Common Stock duly issued upon the exchange or conversion of Debt Securities or Preferred Stock that are exchangeable for or convertible into Common Stock or upon the exercise of Warrants and receipt by the Company of any additional consideration payable upon such conversion, exchange or exercise, but excluding the ATM Shares), upon due execution and delivery on behalf of the Company of certificates therefor, including global certificates, or the entry of the issuance thereof in the books and records of the Company, as the case may be, will be validly issued, fully paid and nonassessable.

(d) The Warrants, upon due execution and delivery of a warrant agreement relating thereto on behalf of the Company and the warrant agent named therein, as applicable, and due authentication of the Warrants

by such warrant agent, as applicable, and upon due execution and delivery of the Warrants on behalf of the Company, will constitute valid and binding obligations of the Company.

(e) The Units, upon due execution and delivery of a unit agreement relating thereto on behalf of the Company, and upon due execution and delivery of one or more certificates bearing such terms on behalf of the Company, will constitute valid and binding obligations of the Company.

(f) The ATM Shares, following (i) issuance of the ATM Shares pursuant to the terms of the ATM Agreement, which such issuance shall not exceed the Maximum Amount (as defined in the ATM Agreement), and (ii) receipt by the Company of the consideration for the ATM Shares specified in the resolutions of the Board of Directors or a committee designated by the Board of Directors, will be validly issued, fully paid and nonassessable.

The opinions expressed in paragraphs (a), (d) and (e) above with respect to the valid and binding nature of obligations may be limited by bankruptcy, insolvency, reorganization, receivership, moratorium or other laws affecting creditors’ rights (including, without limitation, the effect of statutory and other law regarding fraudulent conveyances, fraudulent transfers and preferential transfers) and by the exercise of judicial discretion and the application of principles of equity, good faith, fair dealing, reasonableness, conscionability and materiality (regardless of whether the Securities are considered in a proceeding in equity or at law).

This opinion letter has been prepared for use in connection with the filing of Post-Effective Amendment No. 2 to 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 Post-Effective Amendment No. 2 to the Registration Statement and to the references to this firm under the caption “Legal Matters” in the Base Prospectus and the ATM Agreement Prospectus included in the Registration Statement. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Act.