Exhibit 5.1

Gibson, Dunn & Crutcher LLP   One Embarcadero Center, Suite 2600 San Francisco, CA 94111-3715 Tel 415.393.8200 gibsondunn.com

Client: 06759-00004

April 18, 2024

Spyre Therapeutics, Inc.

221 Crescent Street

Building 23, Suite 105

Waltham, MA 02453

Re: Spyre Therapeutics, Inc.

  Registration Statement on Form S-1

Ladies and Gentlemen:

We have acted as counsel to Spyre Therapeutics, Inc., a Delaware corporation (the “Company”), in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of a Registration Statement on Form S-1 (the “Registration Statement”) pursuant to the Securities Act of 1933, as amended (the “Securities Act”), relating to the resale from time to time by the selling stockholders named therein of (i) up to 22,496,402 shares (the “Common Shares”) of the Company’s common stock, par value $0.0001 per share (“Common Stock”) and (ii) 10,865,000 shares (the “Conversion Shares”) of Common Stock issuable upon the conversion of 271,625 shares of the Company’s Series B preferred stock, par value $0.0001 per share (the “Preferred Stock”).

In arriving at the opinion expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction as being true and complete copies of the originals, of the specimen common stock certificates and such other documents, corporate records, certificates of officers of the Company and of public officials and other instruments as we have deemed necessary or advisable to enable us to render these opinions. In our examination, we have assumed the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to original documents of all documents submitted to us as copies.

Based on the foregoing, and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that the Common Shares are validly issued, fully paid and non-assessable and the Conversion Shares, when issued upon the conversion of the Preferred Stock, will be validly issued, fully paid and non-assessable.

Abu Dhabi • Beijing • Brussels • Century City • Dallas • Denver • Dubai • Frankfurt • Hong Kong • Houston • London • Los Angeles

Munich • New York • Orange County • Palo Alto • Paris • Riyadh • San Francisco • Singapore • Washington, D.C.

We consent to the filing of this opinion as an exhibit to the Registration Statement, and we further consent to the use of our name under the caption “Legal Matters” in the Registration Statement and the prospectus that forms a part thereof. In giving these consents, 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 of the Commission.

Very truly yours,

/s/ Gibson, Dunn & Crutcher LLP