Eversheds Sutherland (US) LLP

700 Sixth Street, NW, Suite 700
Washington, DC 20001-3980

Exhibit 5.1

September 18, 2025

Capital Southwest Corporation

8333 Douglas Avenue, Suite 1100

Dallas, TX 75225

Ladies and Gentlemen:

We have acted as counsel to Capital Southwest Corporation, a Texas corporation (the “Company”), in connection with the Company’s Registration Statement on Form N-2 (File No. 333-282873) filed under the Securities Act of 1933, as amended (the “Securities Act”), which Registration Statement was filed with the Securities and Exchange Commission (the “Commission”) on October 29, 2024, and became effective automatically pursuant to Rule 462(e) under the Securities Act (as amended as of its most recent effective date, including the exhibits and schedules thereto, all documents incorporated or deemed to be incorporated into the Registration Statement by reference, any information contained in a prospectus supplement relating to the Notes (as defined below) subsequently filed with the Commission pursuant to Rule 424 under the Securities Act and deemed to be part of the Registration Statement at the time of effectiveness pursuant to Rule 430B under the Securities Act, any registration statement filed pursuant to Rule 462(b) under the Securities Act, and any post-effective amendment thereto, is hereinafter referred to as the “Registration Statement”) and the Prospectus Supplement (as defined below).

The Registration Statement relates to the public offering of securities of the Company that may be offered by the Company from time to time as set forth in the base prospectus, dated October 29, 2024, which forms part of the Registration Statement, together with the information incorporated or deemed to be incorporated therein by reference (the “Base Prospectus”), and as may be set forth from time to time in one or more supplements to the Base Prospectus. This opinion letter is rendered in connection with the issuance and sale under the Securities Act of $350,000,000 in aggregate principal amount of the Company’s 5.950% Notes due 2030 (the “Notes”), as described in (i) the Base Prospectus and (ii) the prospectus supplement, dated September 9, 2025, relating to the Notes, together with the information incorporated or deemed to be incorporated by reference therein (together with the Base Prospectus, the “Prospectus Supplement”), filed with the Commission pursuant to Rule 424 under the Securities Act. All of the Notes are to be sold by the Company as described in the Registration Statement and the Prospectus Supplement. 

The Notes will be issued pursuant to the indenture, dated as of October 23, 2017 (the “Base Indenture”), by and between the Company and U.S. Bank Trust Company, National Association (as successor in interest to U.S. Bank National Association), as trustee (the “Trustee”), as supplemented by a seventh supplemental indenture, dated as of September 18, 2025 (the “Seventh Supplemental Indenture”, and together with the Base Indenture, the “Indenture”), which Seventh Supplemental Indenture was filed by the Company with the Commission as an exhibit to the Current Report on Form 8-K on the date hereof.

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As counsel to the Company, we have participated in the preparation of the Registration Statement, the Base Prospectus, and the Prospectus Supplement and have examined the originals or copies, certified or otherwise identified to our satisfaction as being true copies, of the following:

(i)the Articles of Incorporation of the Company, as amended, certified as of the date hereof by an officer of the Company;

(ii)the Second Amended and Restated Bylaws of the Company, as amended, certified as of the date hereof by an officer of the Company;

(iii)a Certificate of Fact with respect to the Company issued by the Texas Secretary of State as of a recent date;

(iv)resolutions of the Board of Directors of the Company, or a duly authorized committee thereof, relating to, among other things: (a) the preparation and filing of the Registration Statement and the Prospectus Supplement; (b) the offering, issuance and sale of the Notes, and the terms and conditions thereof; and (c) the authorization of the execution and delivery of the Underwriting Agreement (as defined below), the Indenture, and the transactions contemplated thereby, including, without limitation, the issuance and sale of the Notes, certified as of the date hereof by an officer of the Company;

(v)the underwriting agreement, dated September 9, 2025, by and among the Company and Deutsche Bank Securities Inc., ING Financial Markets LLC, Morgan Stanley & Co. LLC, SMBC Nikko Securities America, Inc., and Wells Fargo Securities, LLC, as representatives of the several underwriters named on Schedule A thereto, relating to the issuance and sale of the Notes (the “Underwriting Agreement”);

(vi)the Indenture; and

(vii)a specimen copy of the form of the Notes to be issued pursuant to the Indenture in the form that was filed by the Company with the Commission as an exhibit to the Current Report on Form 8-K on the date hereof.

 With respect to such examination and our opinion expressed herein, we have assumed, without any independent investigation or verification, (i) the genuineness of all signatures on all documents submitted to us for examination, (ii) the legal capacity of all natural persons, (iii) the authenticity of all documents submitted to us as originals, (iv) the conformity to original documents of all documents submitted to us as conformed or reproduced copies and the authenticity of the originals of such copied documents, (v) that all certificates issued by public officials or officers of the Company have been properly issued, (vi) the accuracy and completeness of all corporate records made available to us by the Company, (vii) that the Indenture will be a valid and legally binding obligation of the parties thereto (other than the Company), and (viii) that at the time of issuance of the Notes, after giving effect to such issuance, the Company will be in compliance with Section 18(a)(1)(A) of the Investment Company Act of 1940, as amended (the “1940 Act”), giving effect to Section 61(a)(2) of the 1940 Act.

As to certain matters of fact relevant to the opinion in this opinion letter, we have relied on certificates of officers of the Company, and on the representations, warranties and covenants of the Company set forth in the Underwriting Agreement. We also have relied on certificates and confirmations of public officials. We have not independently established the facts or, in the case of certificates or confirmations of public officials (which we have assumed remain accurate as of the date of this opinion letter), the other statements, so relied upon.

The opinion set forth below is limited to the contract laws of the State of New York, as in effect on the date hereof, and we express no opinion with respect to any other laws of the State of New York or the laws of any other jurisdiction. Without limiting the preceding sentence, we express no opinion as to any state securities or broker-dealer laws or regulations thereunder relating to the offer, issuance or sale of the Notes. This opinion letter has been prepared, and should be interpreted, in accordance with customary practice followed in the preparation of opinion letters by lawyers who regularly give, and such customary practice followed by lawyers who on behalf of their clients regularly advise opinion recipients regarding, opinion letters of this kind. 

Based upon and subject to the limitations, exceptions, qualifications and assumptions set forth in this opinion letter, we are of the opinion that, when the Notes are duly executed and delivered by duly authorized officers of the Company and duly authenticated by the Trustee, all in accordance with the provisions of the Indenture, and delivered to the purchasers thereof against payment of the agreed consideration therefor, the Notes will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms, except as such enforceability may be limited by applicable bankruptcy, insolvency, reorganization, receivership, moratorium, fraudulent conveyance, and other similar laws affecting the rights and remedies of creditors generally and by general principles of equity (including, without limitation, the availability of specific performance or injunctive relief and the application of concepts of materiality, reasonableness, good faith and fair dealing), regardless of whether considered in a proceeding at law or in equity.

The opinion expressed in this opinion letter is (i) strictly limited to the matters stated in this opinion letter, and without limiting the foregoing, no other opinions are to be inferred; and (ii) only as of the date of this opinion letter, and we are under no obligation, and do not undertake, to advise the Company or any other person or entity either of any change of law or fact that occurs, or of any fact that comes to our attention, after the date of this opinion letter, even though such change or such fact may affect the legal analysis or a legal conclusion in this opinion letter.

We hereby consent to the filing of this opinion letter as an exhibit to the Company’s Current Report on Form 8-K, to be filed with the Commission on the date hereof for incorporation by reference in the Registration Statement, and to the reference to our firm in the “Legal Matters” section in the Prospectus Supplement. We do not admit by giving this consent that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Eversheds Sutherland (US) LLP