Exhibit 5.1

[Letterhead of Eversheds Sutherland (US) LLP]

September 27, 2019

Capital Southwest Corporation

5400 Lyndon B. Johnson Freeway

Suite 1300

Dallas, TX 75240

Ladies and Gentlemen:

We have acted as counsel to Capital Southwest Corporation, a Texas corporation (the “Company”), in connection with the registration statement on Form N-2, as amended (File No. 333-232492) (the “Registration Statement”), filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), previously declared effective by the Commission, relating 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 prospectus dated August 15, 2019, which forms a part of the Registration Statement (the “Prospectus”), and as may be set forth from time to time in one or more supplements to the Prospectus. This opinion letter is rendered in connection with the issuance, and sale under the Securities Act of $65,000,000 in aggregate principal amount of the Company’s 5.375% Notes due 2024 (the “Notes”) as described in the Prospectus and a prospectus supplement dated September 25, 2019, (the “Prospectus Supplement”). All of the Notes are to be sold by the Company as described in the Registration Statement, the Prospectus and the Prospectus Supplement. 

The Notes will be issued pursuant to an indenture, dated October 23, 2017 (the “Base Indenture”), between the Company and U.S. Bank National Association, as trustee (the “Trustee”), as supplemented by a second supplemental indenture, dated September 27, 2019 (the “Second Supplemental Indenture”, and together with the Base Indenture, the “Indenture”), between the Company and the Trustee, which Second Supplemental Indenture was filed by the Company with the Commission as an exhibit to the Current Report on Form 8-K on September 27, 2019 (the “Form 8-K”).

As counsel to the Company, we have participated in the preparation of the Registration Statement, the 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 of this opinion letter 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 any committee thereof relating to, among other things, (a) the authorization and approval of the preparation and filing of the Registration Statement and (b) the authorization, issuance and sale of the Notes;

(v) the Underwriting Agreement, dated September 24, 2019, by and between the Company and Raymond James & Associates, Inc., as representative of the several underwriters listed on Schedule A thereto, relating to the issuance and sale of the Notes;

(vi) the Base Indenture;

(vii) the Second Supplemental Indenture; and

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

 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, and (v) that all certificates issued by public officials have been properly issued. We also have assumed without independent investigation or verification (i) the accuracy and completeness of all corporate records made available to us by the Company and (ii) that the Indenture will be a valid and legally binding obligation of the parties thereto (other than the Company).

As to certain matters of fact relevant to the opinion in this opinion letter, we have relied up certificates and/or representations of officers of the Company. We have also 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, the other statements, so relied upon.

The opinion in this opinion letter is limited to the contract laws of the State of New York, in each case, 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 to 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: (i) is strictly limited to the matters stated in this opinion letter, and without limiting the foregoing, no other opinions are to be inferred; and (ii) is only as of the date of this opinion letter, and we are under no obligation, and do not undertake, to advise the addressee of this opinion letter 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 with the Commission as an exhibit to the Form 8-K, to be filed with the Commission on the date hereof, and to the reference to our firm in the “Legal Matters” section in the Registration Statement and related Prospectus and 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