Exhibit 5.1

750 E. PRATT STREET SUITE 900 BALTIMORE, MD 21202 T 410.244.7400 F 410.244.7742 www.Venable.com

October 25, 2023

Ellington Residential Mortgage REIT

53 Forest Avenue

Old Greenwich, CT 06870

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

We have served as Maryland counsel to Ellington Residential Mortgage REIT, a Maryland real estate investment trust (the “Company"), in connection with certain matters of Maryland law relating to the registration of up to an aggregate of $500,000,000 of the following securities of the Company (collectively, the “Securities”): (i) common shares of beneficial interest, $0.01 par value per share (“Common Shares”); (ii) preferred shares of beneficial interest, $0.01 par value per share (“Preferred Shares”); (iii) debt securities (“Debt Securities”); (iv) depositary shares, each representing a fraction of a Preferred Share (“Depositary Shares”); (v) warrants to purchase Common Shares, Preferred Shares or Depositary Shares (“Warrants”); (vi) rights to purchase Common Shares or Preferred Shares (“Rights”); and (vii) units consisting of any combination of two or more of the foregoing Securities (the “Units”), each covered by the above-referenced Registration Statement, and all amendments thereto (the “Registration Statement”), filed by the Company with the United States Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “1933 Act”).

In connection with our representation of the Company, and as a basis for the opinion hereinafter set forth, we have examined originals, or copies certified or otherwise identified to our satisfaction, of the following documents (hereinafter collectively referred to as the “Documents”):

1.The Registration Statement and the related form of prospectus included therein in the form in which it was transmitted to the Commission for filing under the 1933 Act;

2.The declaration of trust of the Company (the “Declaration of Trust”), certified by the State Department of Assessments and Taxation of Maryland (the “SDAT”);

3.The Second Amended and Restated Bylaws of the Company (the “Bylaws”), certified as of the date hereof by an officer of the Company;

4.The Shareholders’ Agreement, dated as of May 6, 2013 (the “Shareholders Agreement”), by and among the Company, Blackstone Tactical Opportunities EARN Holdings

L.L.C., a Delaware limited liability company, EMG Holdings, L.P., a Delaware limited partnership, any other securityholders of the Company or Unit (as defined in the Shareholders Agreement) holders of the Operating Partnership (as defined in the Shareholders Agreement) who become party to the Shareholders Agreement from time to time pursuant to the terms thereof and Ellington Residential Mortgage Management LLC, a Delaware limited liability company;

5.A certificate of the SDAT as to the good standing of the Company, dated as of a recent date;

6.Resolutions (the “Resolutions”) adopted by the Board of Trustees of the Company (the “Board”) relating to the Securities, certified as of the date hereof by an officer of the Company;

7.A certificate executed by an officer of the Company, dated as of the date hereof; and

8.Such other documents and matters as we have deemed necessary or appropriate to express the opinion set forth below, subject to the assumptions, limitations and qualifications stated herein.

In expressing the opinion set forth below, we have assumed the following:

1.Each individual executing any of the Documents, whether on behalf of such individual or another person, is legally competent to do so.

2.Each individual executing any of the Documents on behalf of a party (other than the Company) is duly authorized to do so.

3.Each of the parties (other than the Company) executing any of the Documents has duly and validly executed and delivered each of the Documents to which such party is a signatory, and the obligations of such party set forth therein are legal, valid and binding and are enforceable in accordance with all stated terms.

4.All Documents submitted to us as originals are authentic. The form and content of all Documents submitted to us as unexecuted drafts do not differ in any respect relevant to this opinion from the form and content of such Documents as executed and delivered. All Documents submitted to us as certified or photostatic copies conform to the original documents. All signatures on all Documents are genuine. All public records reviewed or relied upon by us or on our behalf are true and complete. All representations, warranties, statements and information contained in the Documents are true and complete. There has been no oral or written modification of or amendment to any of the Documents, and there has been no waiver of any provision of any of the Documents, by action or omission of the parties or otherwise.

5.The issuance, and certain terms, of any Securities to be issued by the Company from time to time will be authorized and approved by the Board, or a duly authorized committee thereof, in accordance with the Maryland REIT Law, the Declaration of Trust, the Bylaws and the Resolutions and, in the case of any Securities that are Preferred Shares of any class or series (“Preferred Securities”), including any Preferred Securities represented by Depositary Shares or issued upon conversion, exchange, exercise or redemption of any other Securities convertible into, or exchangeable, exercisable or redeemable for, Preferred Securities, Articles Supplementary designating the class or series of Preferred Shares and setting forth the authorized number and the terms thereof (the “Articles Supplementary”) will be filed with and accepted for record by the SDAT prior to the issuance of such Preferred Securities (such approval and, if applicable, filing and acceptance for record, referred to herein as the “Trust Proceedings”).

6.Upon the issuance of any Securities that are Common Shares (“Common Securities”), including Common Securities which may be issued upon conversion, exercise, exchange or redemption of any other Securities convertible into, or exchangeable, exercisable or redeemable for, Common Securities, the total number of Common Shares issued and outstanding will not exceed the total number of Common Shares that the Company is then authorized to issue under the Declaration of Trust.

7.Upon the issuance of any Preferred Securities, including any Preferred Securities represented by Depositary Shares or issued upon conversion, exercise, exchange or redemption of any other Securities convertible into, or exchangeable, exercisable or redeemable for, Preferred Securities, the total number of Preferred Shares issued and outstanding, and the total number of Preferred Shares of the applicable class or series issued and outstanding, will not exceed the total authorized number of Preferred Shares or the total authorized number of such class or series of Preferred Shares that the Company is then authorized to issue under the Declaration of Trust.

8.None of the Securities will be issued or transferred in violation of the restrictions on transfer and ownership contained in Article VII of the Declaration of Trust or any comparable provision in the Articles Supplementary designating any class or series of Preferred Shares.

9.Any Securities convertible into, or exercisable, exchangeable or redeemable for, any other Securities will be duly converted, exercised, exchanged or redeemed in accordance with their terms.

Based upon the foregoing, and subject to the assumptions, limitations and qualifications stated herein, it is our opinion that:

1.The Company is a real estate investment trust duly formed and existing under and by virtue of the laws of the State of Maryland and is in good standing with the SDAT.

2.Upon the completion of all Trust Proceedings relating to the Common Securities, the issuance of such Common Securities will be duly authorized and, when and if issued and delivered against payment therefor in accordance with the Registration Statement, the Resolutions and the Trust Proceedings, the Common Securities will be validly issued, fully paid and nonassessable.

3.Upon the completion of all Trust Proceedings relating to the Preferred Securities, the issuance of such Preferred Securities will be duly authorized and, when and if issued and delivered against payment therefor in accordance with the Registration Statement, the Resolutions and the Trust Proceedings, the Preferred Securities will be validly issued, fully paid and nonassessable.

4.Upon the completion of all Trust Proceedings relating to the Securities that are Depositary Shares, the issuance of the Depositary Shares will be duly authorized.

5.Upon the completion of all Trust Proceedings relating to the Warrants, the issuance of the Warrants will be duly authorized.

6.Upon the completion of all Trust Proceedings relating to the Rights, the issuance of the Rights will be duly authorized.

7.Upon the completion of all Trust Proceedings relating to the Units, including all Trust Proceedings relating to the Securities sold together as Units, the issuance of the Units will be duly authorized.

The foregoing opinion is limited to the laws of the State of Maryland and we do not express any opinion herein concerning any federal law or the laws of any other jurisdiction. We express no opinion as to the applicability or effect of federal or state securities laws, including the securities laws of the State of Maryland, federal or state laws regarding fraudulent transfersor the laws, codes or regulations of any municipality or other local jurisdiction. To the extent that any matter as to which our opinion is expressed herein would be governed by the laws of any jurisdiction other than the State of Maryland, we do not express any opinion on such matter. The opinion expressed herein is subject to the effect of any judicial decision which may permit the introduction of parol evidence to modify the terms or the interpretation of agreements.

The opinion expressed herein is limited to the matters specifically set forth herein and no other opinion shall be inferred beyond the matters expressly stated. We assume no obligation to supplement this opinion if any applicable law changes after the date hereof or if we become aware of any fact that might change the opinion expressed herein after the date hereof.

This opinion is being furnished to you for submission to the Commission as an exhibit to the Registration Statement. We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the use of the name of our firm therein. In giving

this consent, we do not admit that we are within the category of persons whose consent is required by Section 7 of the 1933 Act.

Very truly yours,

/s/ Venable LLP