Exhibit 5.1

[Letterhead of Eversheds Sutherland (US) LLP]

August 4, 2022

Capital Southwest Corporation

8333 Douglas Avenue

Suite 1100

Dallas, Texas 75225

Re:   Capital Southwest Corporation

Registration Statement on Form S-8

Ladies and Gentlemen:

We have acted as counsel to Capital Southwest Corporation, a Texas corporation (the “Company”), in connection with the preparation and filing by the Company with the Securities and Exchange Commission of a registration statement on Form S-8 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), with respect to the offer and sale of up to 120,000 shares of the Company’s common stock, par value $0.25 per share (the “Shares”), pursuant to the Capital Southwest Corporation 2021 Non-Employee Director Restricted Stock Award Plan (the “Plan”).

As counsel to the Company, we have participated in the preparation of the Registration Statement and have examined originals or 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 issued by the Office of the Secretary of State of Texas as to the existence of the Company, as of a recent date; and

(iv)the resolutions of the board of directors of the Company relating to, among other things, (a) the authorization and approval of the preparation and filing of the Registration Statement and (b) the authorization, issuance, offer and sale of the Shares pursuant to the Registration Statement and the Plan.

With respect to such examination and our opinion expressed in this opinion letter, 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, and (v) that all certificates issued by public officials have been properly issued. We also have assumed without independent investigation or verification the accuracy and completeness of all corporate records made available to us by the Company.

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

The opinions set forth below are limited to the effect of the Texas Business Organizations Code, as in effect on the date of this opinion letter, and we express no opinion as to the applicability or effect of any other laws of the State of Texas or the laws of any other jurisdictions. 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 and sale of the Shares pursuant to the Registration Statement and the Plan. 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 the Shares issuable pursuant to the Registration Statement and the Plan have been duly authorized and, when issued and paid for in accordance with the terms of the Plan, the Shares will be validly issued, fully paid and nonassessable.

Capital Southwest Corporation

August 4, 2022

Page 2

The opinions expressed in this opinion letter (a) are strictly limited to the matters stated in this opinion letter, and without limiting the foregoing, no other opinions are to be inferred and (b) are 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 Registration Statement. 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 and the rules and regulations thereunder.

Respectfully submitted,

/s/ Eversheds Sutherland (US) LLP