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Exhibit 5.1

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 statement on Form S-3 (the “Registration Statement”) to be filed on the date hereof by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933 (the “Securities Act”). The Registration Statement relates to the issuance and sale by the Company from time to time, pursuant to Rule 415 of the General Rules and Regulations of the Commission promulgated under the Securities Act (the “Rules and Regulations”), of (i) shares of common stock, par value $0.01 per share, of the Company (“Common Stock”), (ii) shares of preferred stock, par value $0.01 per share, of the Company (“Preferred Stock”), which may be issued in one or more classes or series, (iii) depositary receipts (the “Receipts”) representing fractional shares of Preferred Stock, which are called depositary shares (the “Depositary Shares”) and which may be issued pursuant to one or more depositary agreements (each, a “Depositary Agreement”) proposed to be entered into between the Company and one or more bank or trust companies to be named in the applicable Depositary Agreement (each, a “Bank Depositary”); (iv) debt securities of the Company (“Debt Securities”), which may be issued in one or more series under an indenture (the “Indenture”) proposed to be entered into by the Company and the trustee to be named therein, the form of which is filed as an exhibit to the Registration Statement, (v) warrants to purchase shares of Common Stock, shares of Preferred Stock or Debt Securities (“Warrants”), which may be issued pursuant to one or more warrant agreements (each, a “Warrant Agreement”) proposed to be entered into by the Company and one or more warrant agents to be named therein, (vi) subscription rights to purchase shares of Common Stock, shares of Preferred Stock or Debt Securities (“Subscription Rights”), which may be issued under one or more subscription rights certificates (each, a “Subscription Rights Certificate”) and/or pursuant to one or more subscription rights agreements (each, a “Subscription Rights Agreement”) proposed to be entered into by the Company and one or more subscription agents to be named therein, (vii) purchase contracts (“Purchase Contracts”) obligating the holders thereof to purchase from the Company, and the Company to sell to such holders, shares of Common Stock, shares of Preferred Stock or Debt Securities at a future date or dates, which may be issued pursuant to one or more purchase contract agreements (each, a “Purchase Contract Agreement”) proposed to be entered into by the Company and one or more purchase contract agents to be named therein, (viii) purchase units of the Company (“Purchase Units”), each consisting of a Purchase Contract and Debt Securities, preferred securities or debt obligations of third-parties, including U.S. treasury securities, or any combination of the foregoing, securing the holder’s obligation to purchase Common Stock or the Company’s other securities, which may be issued pursuant to one or more agreements (each, a “Purchase Unit Agreement”) proposed to be entered into by the Company and one or more purchase unit agents to be named therein, and (ix) such indeterminate number of shares of Common Stock, Preferred Stock or Depositary Shares and indeterminate amount of Debt Securities as may be issued upon conversion, exchange or exercise, as applicable, of any Preferred Stock, Depositary Shares, Debt Securities, Warrants or Subscription Rights or settlement of any Purchase Contracts or Purchase Units, including such shares of Common Stock or Preferred Stock as may be issued pursuant to anti-dilution adjustments determined at the time of the offering (collectively, “Indeterminate Securities”). The Common Stock, Preferred Stock, Depositary Shares, Debt Securities, Warrants, Subscription Rights, Purchase Contracts, Purchase Units and Indeterminate Securities offered pursuant to the Registration Statement are collectively referred to herein as the “Securities”.

Rithm Capital Corp.

August 1, 2025

Page 2

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

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

(a)          the Registration Statement;

(b)          the form of Indenture filed as an exhibit to the Registration Statement;

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

(d)          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;

(e)          a copy of the Company’s Amended and Restated By-laws, as amended and in effect as of the date hereof (the “Amended and Restated Bylaws”) and certified pursuant to the Secretary’s Certificate; and

(f)          a copy of certain resolutions of the Board of Directors of the Company, adopted on July 31, 2025, 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, including the facts and conclusions set forth in the Secretary’s Certificate.

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 and the Amended and Restated Certificate.

We do not express any opinion with respect to the laws of any jurisdiction other than (i) the laws of the State of New York and (ii) the General Corporation Law of the State of Delaware (the “DGCL”) (all of the foregoing being referred to as “Opined-on Law”). The Securities may be issued from time to time on a delayed or continuous basis, and this opinion letter 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.

As used herein, “Transaction Documents” means the Depositary Agreements, the Indenture and the supplemental indentures and officer’s certificates establishing the terms of the Debt Securities pursuant thereto, the Warrant Agreements, the Subscription Rights Agreements, the Purchase Contract Agreements, the Purchase Unit Agreements and any applicable underwriting or purchase agreement.

The opinions stated in paragraphs 1 through 8 below presume that all of the following (collectively, the “general conditions”) shall have occurred prior to the issuance of the Securities referred to therein: (i) the Registration Statement, as finally amended (including all necessary post-effective amendments), has become effective under the Securities Act; (ii) an appropriate prospectus supplement or term sheet with respect to such Securities has been prepared, delivered and filed in compliance with the Securities Act and the applicable Rules and Regulations; (iii) the applicable Transaction Documents shall have been duly authorized, executed and delivered by the Company and the other parties thereto, including, if such Securities are to be sold or otherwise distributed pursuant to a firm commitment underwritten offering, the underwriting agreement or purchase agreement with respect thereto; (iv) the Board of Directors of the Company, including any duly authorized committee thereof, shall have taken all necessary corporate action to approve the issuance and sale of such Securities and related matters and appropriate officers of the Company have taken all related action as directed by or under the direction of the Board of Directors of the Company; and (v) the terms of the applicable Transaction Documents and the issuance and sale of such Securities have been duly established in conformity with the Amended and Restated Certificate so as not to violate any applicable law, the Amended and Restated Certificate or the Amended and Restated Bylaws, or result in a default under or breach of any agreement or instrument binding upon the Company or its properties, and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company or its properties.

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

1.          With respect to any shares of Common Stock offered by the Company, including any Indeterminate Securities constituting Common Stock (the “Offered Common Stock”), when (a) the general conditions shall have been satisfied, (b) if the Offered Common Stock is to be certificated, certificates in the form required under the DGCL representing the shares of Offered Common Stock are duly executed and countersigned or, if the Offered Common Stock is to be issued in uncertificated form, a resolution of the Board of Directors has duly authorized the issuance of the Offered Common Stock in uncertificated form and (c) the shares of Offered Common Stock are registered in the Company’s share registry and delivered upon payment of the agreed-upon consideration therefor, the shares of Offered Common Stock, when issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document, will be duly authorized by all requisite corporate action on the part of the Company under the DGCL and validly issued, fully paid and nonassessable, provided that the consideration therefor is not less than $0.01 per share of Common Stock.

2.          With respect to the shares of any series of Preferred Stock offered by the Company, including any Indeterminate Securities constituting Preferred Stock of such series (the “Offered Preferred Stock”), when (a) the general conditions shall have been satisfied, (b) the Board of Directors of the Company, or a duly authorized committee thereof, has duly adopted a Certificate of Designations for the Offered Preferred Stock in accordance with the DGCL (the “Certificate”), (c) the filing of the Certificate with the Secretary of State of the State of Delaware has duly occurred, (d) if the Offered Preferred Stock is to be certificated, certificates in the form required under the DGCL representing the shares of Offered Preferred Stock are duly executed and countersigned or, if the Offered Preferred Stock is to be issued in uncertificated form, a resolution of the Board of Directors has duly authorized the issuance of the Offered Preferred Stock in uncertificated form and (e) the shares of Offered Preferred Stock are registered in the Company’s share registry and delivered upon payment of the agreed-upon consideration therefor, the shares of Offered Preferred Stock, when issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document, will be duly authorized by all requisite corporate action on the part of the Company under the DGCL and validly issued, fully paid and nonassessable, provided that the consideration therefor is not less than $0.01 per share of Preferred Stock.

3.          With respect to any Depositary Shares offered by the Company, including any Indeterminate Securities constituting Depositary Shares (the “Offered Depositary Shares”), when (a) the general conditions shall have been satisfied, (b) the Preferred Stock relating to such Offered Depositary Shares has been duly authorized for issuance by the Company; (c) the Offered Depositary Shares have been duly executed, delivered, countersigned, issued and sold in accordance with the provisions of the applicable Depositary Agreement, and the Offered Depositary Shares have been delivered to the Bank Depositary for deposit in accordance with the applicable Depositary Agreement; and (d) the Receipts evidencing the Depositary Shares have been duly issued against deposit of the related shares of Preferred Stock with the Bank Depositary in accordance with the applicable Depositary Agreement, the Offered Depositary Shares evidenced by such Receipts will entitle the registered holder thereof to the rights specified in such Receipt and in the Depositary Agreement.

4.          With respect to any series of Debt Securities offered by the Company, including any Indeterminate Securities constituting Debt Securities of such series (the “Offered Debt Securities”), when (a) the general conditions shall have been satisfied, (b) the Indenture has been qualified under the Trust Indenture Act of 1939, (c) the issuance, sale and terms of the Offered Debt Securities and related matters have been approved and established in conformity with the applicable Transaction Documents and (d) the certificates evidencing the Offered Debt Securities have been issued in a form that complies with the provisions of the applicable Transaction Documents and have been duly executed and authenticated in accordance with the provisions of the Indenture and any other applicable Transaction Documents and issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document upon payment of the agreed-upon consideration therefor, the Offered Debt Securities will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms under the laws of the State of New York.

5.          With respect to any Warrants offered by the Company (the “Offered Warrants”), when (a) the general conditions shall have been satisfied, (b) the Common Stock, Preferred Stock and/or Debt Securities for which the Offered Warrants are exercisable have been duly authorized for issuance by the Company and (c) certificates evidencing the Offered Warrants have been duly executed, delivered and countersigned in accordance with the provisions of the applicable Warrant Agreement, the Offered Warrants, when issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document upon payment of the agreed-upon consideration therefor, will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms under the laws of the State of New York.

6.          With respect to any Subscription Rights offered by the Company (the “Offered Subscription Rights”), when (a) the general conditions shall have been satisfied, (b) the Common Stock, Preferred Stock and/or Debt Securities relating to such Offered Subscription Rights have been duly authorized for issuance by the Company and (c) the Subscription Rights Certificates have been duly executed, delivered and countersigned in accordance with the provisions of the applicable Subscription Rights Agreement, the Offered Subscription Rights, when issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document upon payment of the agreed-upon consideration therefor, will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms under the laws of the State of New York.

7.          With respect to any Purchase Contracts offered by the Company (the “Offered Purchase Contracts”), when (a) the general conditions shall have been satisfied, (b) the Common Stock, Preferred Stock and/or Debt Securities relating to such Offered Purchase Contracts have been duly authorized for issuance by the Company and (c) the Offered Purchase Contracts have been duly executed, delivered and countersigned in accordance with the provisions of the applicable Purchase Contract Agreement, the Offered Purchase Contracts, when issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document upon payment of the agreed-upon consideration therefor, will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms under the laws of the State of New York.

8.          With respect to any Purchase Units offered by the Company (the “Offered Purchase Units”), when (a) the general conditions shall have been satisfied, (b) a Purchase Contract and Debt Securities, preferred securities or debt obligations of third-parties, including U.S. treasury securities, or any combination of the foregoing, securing the holder’s obligation to purchase the Company’s Common Stock or other securities under the Purchase Contracts included in such Offered Purchase Units have been duly authorized for issuance or sale, as applicable, by the Company and (c) certificates evidencing the Offered Purchase Units have been duly executed, delivered and countersigned in accordance with the provisions of the applicable Purchase Unit Agreement, the Offered Purchase Units, when issued and sold or otherwise distributed in accordance with the provisions of the applicable Transaction Document upon payment of the agreed-upon consideration therefor, will constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their respective terms under the laws of the State of New York.

The opinions stated herein are subject to the following assumptions and qualifications:

(a)          we do not express any opinion with respect to the effect on the opinions stated herein of any bankruptcy, insolvency, reorganization, moratorium, fraudulent transfer, preference and other similar laws or governmental orders affecting creditors’ rights generally, and the opinions stated herein are limited by such laws and governmental orders and by general principles of equity (regardless of whether enforcement is sought in equity or at law);

(b)          we do not express any opinion with respect to any law, rule or regulation that is applicable to any party to any of the Transaction Documents or the transactions contemplated thereby solely because such law, rule or regulation is part of a regulatory regime applicable to any such party or any of its affiliates as a result of the specific assets or business operations of such party or such affiliates;

(c)          except to the extent expressly stated in the opinions contained herein, we have assumed that each of the Transaction Documents constitutes the valid and binding obligation of each party to such Transaction Document, enforceable against such party in accordance with its terms;

(d)          we do not express any opinion with respect to the enforceability of any provision contained in any Transaction Document relating to any indemnification, contribution, non-reliance, exculpation, release, limitation or exclusion of remedies, waiver or other provisions having similar effect that may be contrary to public policy or violative of federal or state securities laws, rules or regulations, or to the extent any such provision purports to, or has the effect of, waiving or altering any statute of limitations;

(e)          we do not express any opinion with respect to the enforceability of any provision of any Transaction Document to the extent that such provision purports to bind the Company to the exclusive jurisdiction of any particular court or courts;

(f)          we call to your attention that irrespective of the agreement of the parties to any Transaction Document, a court may decline to hear a case on grounds of forum non conveniens or other doctrine limiting the availability of such court as a forum for resolution of disputes; in addition, we call to your attention that we do not express any opinion with respect to the subject matter jurisdiction of the federal courts of the United States of America in any action arising out of or relating to any Transaction Document;

(g)          the opinions stated herein are limited to the agreements and documents specifically identified in the opinions contained herein (the “Specified Documents”) without regard to any agreement or other document referenced in any such Specified Document (including agreements or other documents incorporated by reference or attached or annexed thereto) and without regard to any other agreement or document relating to any such Specified Document that is not a Transaction Document;

(h)          subsequent to the effectiveness of the Indenture and immediately prior to the issuance of any series of Debt Securities, the Indenture has not been amended, restated, supplemented or otherwise modified in any way that affects or relates to such series of Debt Securities other than by the applicable Transaction Documents relating to such series of Debt Securities;

(i)          we have assumed that the laws of the state of New York will be chosen to govern any Transaction Documents entered into subsequent to the date hereof and that such choice is and will be a valid and legal provision;

(j)          we have assumed that the Indenture will be duly authorized, executed and delivered by the trustee in substantially the form reviewed by us; and

(k)          to the extent that any opinion relates to the enforceability of the choice of New York law and choice of New York forum provisions contained in any Transaction Document, the opinions stated herein are subject to the qualification that such enforceability may be subject to, in each case, (i) the exceptions and limitations in New York General Obligations Law Sections 5-1401 and 5-1402 and (ii) principles of comity and constitutionality.

In addition, in rendering the foregoing opinions we have further assumed that:

(a)          neither the execution and delivery by the Company of the Transaction Documents nor the performance by the Company of its obligations thereunder, including the issuance and sale of the applicable Securities: (i) conflicts or will conflict with the Amended and Restated Certificate or the Amended and Restated Bylaws of the Company, (ii) constitutes or will constitute a violation of, or a default under, any lease, indenture, agreement or other instrument to which the Company or its property is subject, (iii) contravenes or will contravene any order or decree of any governmental authority to which the Company or its property is subject, or (iv) violates or will violate any law, rule or regulation to which the Company or its property is subject (except that we do not make the assumption set forth in this clause (iv) with respect to the Opined-on Law); and

(b)          neither the execution and delivery by the Company of the Transaction Documents nor the performance by the Company of its obligations thereunder, including the issuance and sale of the applicable Securities, requires or will require the consent, approval, licensing or authorization of, or any filing, recording or registration with, any governmental authority under any law, rule or regulation of any jurisdiction.

We hereby consent to the reference to our firm under the heading “Legal Matters” in the prospectus forming part of the Registration Statement. We also hereby consent to the filing of this opinion letter with the Commission as an exhibit to 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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