Exhibit 5.1

Skadden, Arps, Slate, Meagher & Flom llp

ONE MANHATTAN WEST

NEW YORK, NY 10001

TEL: (212) 735-3000

FAX: (212) 735-2000

www.skadden.com

August 1, 2025

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 registration of up to 14,423,655 shares of the Company’s common stock, par value $0.01 per share (“Common Stock”), consisting of an aggregate of 14,423,655 shares of Common Stock (the “Shares”) which may be issued upon the exercise of stock options granted under the Rithm Capital Corp. Nonqualified Stock Option and Incentive Award Plan adopted as of February 16, 2023 (as amended and/or restated as of the date hereof, the “Plan”).

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”).

August 1, 2025

Page 2

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, among other things, the issuance and sale of the Shares from time to time, filed on August 1, 2025 with the Securities and Exchange Commission (the “Commission”) 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 the 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”);

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

(c)          the prospectus supplement, dated August 1, 2025 (together with the Base Prospectus, the “Prospectus”), relating to the offering of the Shares, in the form filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations;

(d)          the Plan;

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

(f)          a copy of the Company’s Amended and Restated Certificate of Incorporation (the “Amended and Restated Certificate”), certified by the Secretary of State of the State of Delaware as of July 31, 2025, and certified pursuant to the Secretary’s Certificate;

(g)          a copy of the Company’s Amended and Restated Bylaws, as amended and in effect as of August 1, 2025 (the “Amended and Restated Bylaws”), and certified pursuant to the Secretary’s Certificate;

(h)          a copy of certain resolutions of the Board of Directors of the Company relating to adoption of the Plan, adopted on February 7, 2023, certified pursuant to the Secretary’s Certificate; and

(i)          a copy of certain resolutions of the Board of Directors of the Company relating to the sale or resale (as the case may be) of the Shares, adopted on July 31, 2025, in each case 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 opinion stated below.

August 1, 2025

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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.  In making our examination of executed documents, we have assumed that the parties thereto, other than the Company, had the power, corporate or other, to enter into and perform all obligations thereunder and have also assumed the due authorization by all requisite action, corporate or other, and the execution and delivery by such parties of such documents and the validity and binding effect thereof on such parties. As to any facts relevant to the opinion 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 Amended and Restated Certificate and the Secretary’s Certificate.

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”). The Shares may be sold from time to time on a delayed or continuous basis, and this opinion is limited to the laws, including the rules and regulations, as in effect on the date hereof, which laws are subject to change with possible retroactive effect.

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that the Shares 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 Plan, will be validly issued, fully paid and nonassessable.

In addition, in rendering the foregoing opinion we have assumed:

(a)          that each agreement under which options are granted or awards of shares of Common Stock are made pursuant to the Plan is consistent with the Plan and has been duly authorized, executed and delivered by the parties thereto (including the Company);

(b)          the due and proper exercise of any outstanding stock options granted under the Plan in accordance with the terms thereof;

(c)          that the consideration received by the Company in respect of the issuance of all Shares has or will be as determined by the Board of Directors and was or will not be less than the par value of the Common Stock;

(d)          that an appropriate account statement evidencing the Shares credited to the recipient’s account maintained with the Company’s transfer agent will be issued by the Company’s transfer agent and the issuance of the Shares will be properly recorded in the books and records of the Company;

August 1, 2025

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(e)          that the Company’s issuance of the Securities does not (i) except to the extent expressly stated in the opinion 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 Amended and Restated Certificate or the Amended and Restated Bylaws and 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 we have further assumed that the Company will continue to have sufficient authorized shares of Common Stock; and

(f)          the Company’s authorized capital stock is as set forth in the Amended and Restated Certificate, and we have relied solely on the certified copy thereof issued by the Secretary of State of the State of Delaware and have not made any other inquiries or investigations.

We hereby consent to the reference to our firm under the heading “Legal Matters” in 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.

MJS

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