Exhibit 5.1

March 28, 2013

Texas Capital Bancshares, Inc.

2000 McKinney Avenue, Suite 700

Dallas, TX 75201

Ladies and Gentlemen:

We have acted as legal counsel to Texas Capital Bancshares, Inc., (the “Company”) in connection with the public offering of 6,000,000 shares (the “Shares”) of 6.50% Non-Cumulative Perpetual Preferred Stock, Series A, $0.01 par value (“Preferred Stock”), of the Company pursuant to a prospectus supplement dated March 21, 2013 and the accompanying prospectus dated October 25, 2012 (such documents, collectively, the “Prospectus”) that form part of the Company’s effective registration statement on Form S-3, (File No. 333-184586) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission under the Securities Act of 1933, as amended.

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act of 1933, as amended (the “Securities Act”).

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of (i) the Registration Statement, (ii) the Prospectus, (iii) a specimen certificate representing the Preferred Stock, (iv) the Certificate of Incorporation, as amended, of the Company, as currently in effect, (v) the Bylaws, as amended, of the Company, as currently in effect, (vi) the Certificate of Designation for the Preferred Stock, and (vii) certain resolutions adopted by the Board of Directors, or a committee thereof, of the Company with respect to the issuance of the Shares. We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates of public officials, certificates of officers or other representatives of the Company and others, and such other documents, certificates and records, as we have deemed necessary or appropriate as a basis for the opinion set forth herein.

In our examination, we have assumed and have not verified (i) the legal capacity of all natural persons, (ii) the genuineness of all signatures (other than persons signing on behalf of the Company), (iii) the authenticity of all documents submitted to us as originals, (iv) the conformity with the originals of all documents supplied to us as copies, (v) the accuracy and completeness of all corporate records and documents made available to us by the Company, and (vi) that the foregoing documents, in the form submitted to us for our review, have not been altered or amended in any respect material to our opinion stated herein. We have relied as to factual matters upon certificates from officers of the Company and certificates and other documents

Texas Capital Bancshares, Inc.

March 28, 2013

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from public officials and government agencies and departments and we have assumed the accuracy and authenticity of such certificates and documents. We have further assumed that the Shares were issued and delivered in accordance with the terms of the Underwriting Agreement, dated March 26, 2013, among the Company, Morgan Stanley & Co LLC, Merrill Lynch, Pierce, Fenner & Smith Incorporated and J.P. Morgan Securities LLC as representatives of the underwriters.

The following opinion is limited in all respects to matters of the Delaware General Corporation Law and U.S. federal law, and we express no opinion as to the laws of any other jurisdiction.

Based on the foregoing, and subject to the assumptions, qualifications and limitations set forth herein, as of the date hereof, we are of the opinion that the Shares have been duly authorized, validly issued, fully paid and nonassessable.

We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement. We also consent to the reference to our firm under the caption “Legal Matters” in the Prospectus Supplement. In giving this consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission.

Very truly yours,

WINSTEAD PC