Exhibit 5.1

January 21, 2026

Rithm Capital Corp.

799 Broadway

New York, New York 10003

Ladies and Gentlemen:

We have acted as special United States counsel to Rithm Capital Corp., a Delaware corporation (the “Company”), in connection with the public offering by the Company of 10,000,000 shares (the “Firm Shares”) of the Company’s 8.750% Series F Fixed-Rate Reset Cumulative Redeemable Preferred Stock, par value $0.01 per share (“Preferred Stock”), and up to an additional 1,500,000 shares (the “Option Shares”) of the Preferred Stock at the option of the Underwriters (as defined below). The Firm Shares and the Option Shares are collectively referred to herein as the “Securities.”

This opinion letter is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act of 1933 (the “Securities Act”).

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

(a)           the registration statement on Form S-3 (File No. 333-289162) of the Company relating to the Common Stock and other securities of the Company filed with the Securities and Exchange Commission (the “Commission”) on August 1, 2025 under the Securities Act allowing for delayed offerings pursuant to Rule 415 of the General Rules and Regulations under the Securities Act (the “Rules and Regulations”), including information deemed to be a part of the registration statement pursuant to Rule 430B of the Rules and Regulations (such registration statement being hereinafter referred to as the “Registration Statement”);

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January 21, 2026
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(b)           the prospectus, dated August 1, 2025 (the “Base Prospectus”), which forms a part of and is included in the Registration Statement;

(c)           the preliminary prospectus supplement, dated January 13, 2026 (together with the Base Prospectus, the “Preliminary Prospectus”), relating to the offering of the Securities, in the form filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations;

(d)           the prospectus supplement, dated January 13, 2026 (together with the Base Prospectus, the “Prospectus”), relating to the offering of the Securities, in the form filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations;

(e)           an executed copy of the Underwriting Agreement, dated January 13, 2026 (the “Underwriting Agreement”), by and between the Company and Morgan Stanley & Co. LLC, as representative of the several Underwriters named therein (the “Underwriters”), relating to the sale by the Company to the Underwriters of the Securities;

(f)            an executed copy of a certificate of Philip Sivin, Secretary of the Company, dated the date hereof (the “Secretary’s Certificate”);

(g)           a copy of the Company’s Amended and Restated Certificate of Incorporation (the “Certificate of Incorporation”), certified by the Secretary of State of the State of Delaware as of January 13, 2026, and certified pursuant to the Secretary’s Certificate as being in effect on the date of the written consents referred to below and as of the date hereof;

(h)           a copy of the Company’s amended and restated bylaws, as amended (the “Bylaws”), certified pursuant to the Secretary’s Certificate as being in effect on the date of the written consents referred to below and as of the date hereof;

(i)            a copy of certain actions by written consent adopted by the Board of Directors of the Company, dated as of January 9, 2026, and a copy of a written consent of the Pricing Committee of the Board of Directors of the Company, dated as of January 13, 2026,

(j)            an executed certificate evidencing the Securities, registered in the name of Cede & Co; and

(k)           the Certificate of Designations (the “Certificate of Designations”) relating to the Preferred Stock, certified by the Secretary of State of the State of Delaware as of January 21, 2026, and certified pursuant to the Secretary’s Certificate.

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.

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January 21, 2026
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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, the Certificate of Incorporation and the Certificate of Designations and the factual representations and warranties set forth in the Underwriting Agreement.

We do not express any opinion with respect to the laws of any jurisdiction other than the General Corporation Law of the State of Delaware (the “DGCL”).

As used herein, “Organizational Documents” means those documents listed in paragraphs (g) and (h) above.

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that:

1.             The Securities have been duly authorized by all requisite corporate action on the part of the Company under the DGCL and, when the Preferred Stock Certificate is duly executed and delivered against payment therefor in accordance with the terms of the Underwriting Agreement, the Securities will be validly issued, fully paid and nonassessable.

2.             The maximum number of 50,438,540 shares (the “Conversion Shares”) of the Company’s common stock, par value $0.01 per share (the “Common Stock”), issuable upon conversion of the Securities pursuant to the Certificate of Designations have been duly authorized by all requisite corporate action on the part of the Company under the DGCL and, when issued in accordance with the Certificate of Designations, will be validly issued, fully paid and nonassessable.

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

(a)           the Company’s issuance of the Securities does not and the Company’s issuance of the Securities and the Conversion Shares will not (i) except to the extent expressly stated in the opinions contained herein, violate any statute to which the Company or such issuance is subject, or (ii) constitute a violation of, or a breach under, or require the consent or approval of any other person under, any agreement or instrument binding on the Company (except that we do not make this assumption with respect to the Organizational Documents or those agreements or instruments expressed to be governed by the laws of the State of New York which are listed in Part II of the Registration Statement or the Company’s Annual Report on Form 10-K for the year ended December 31, 2024, although we have assumed compliance with any covenant, restriction or provision with respect to financial ratios or tests or any aspect of the financial condition or results of operations of the Company contained in such agreements or instruments) and that the Company will continue to have sufficient authorized shares of Common Stock; and

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January 21, 2026
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(b)           the Company’s authorized capital stock is as set forth in the Certificate of Incorporation and the Certificate of Designations, and we have relied solely on the copies thereof issued by the Secretary of State of the State of Delaware and have not made any other inquiries or investigations.

This opinion letter shall be interpreted in accordance with customary practice of United States lawyers who regularly give opinions in transactions of this type.

We hereby consent to the reference to our firm under the heading “Legal Matters” in the Preliminary Prospectus and the Prospectus. We also hereby consent to the filing of this opinion letter with the Commission as an exhibit to the Company’s Current Report on Form 8-K being filed on the date hereof and incorporated by reference into 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 letter 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.