Exhibit 5.1

[TBI Letterhead]

October 27, 2014

Triumph Bancorp, Inc.

12700 Park Central Drive, Suite 1700

Dallas, Texas 75251

Ladies and Gentlemen:

I am the General Counsel of Triumph Bancorp, Inc., a Texas corporation (the “Company”), and as such have acted as counsel to the Company in connection with the initial public offering of up to 7,705,000 shares of common stock, par value $0.01 per share, of the Company (the “Securities”), pursuant to a Registration Statement on Form S-1 (File No. 333-198838) filed with the U.S. Securities and Exchange Commission (the “SEC”) on September 19, 2014, as amended through the date hereof (the “Registration Statement,” which term does not include any other document or agreement whether or not specifically referred to therein or attached as an exhibit or schedule thereto), relating to the registration of the sale of such Securities under the U.S. Securities Act of 1933, as amended (the “Securities Act”). In connection with the foregoing, you have requested my opinion with respect to the following matters.

For the purposes of giving the opinion contained herein, I, or attorneys working under my direction, have examined the Registration Statement and the form of Underwriting Agreement, between the Company and the underwriters named therein (the “Underwriting Agreement”). I, or attorneys working under my direction, have also examined the originals, or duplicates or certified or conformed copies, of such corporate records, agreements, documents and other instruments, including the amended and restated certificate of formation and amended and restated bylaws of the Company, and have made such other investigations as I have deemed relevant and necessary in connection with the opinion set forth below. As to questions of fact material to this opinion, I have relied, with your approval, upon oral and written representations of officers and representatives of the Company and certificates or comparable documents of public officials and of officers and representatives of the Company.

In making such examination and rendering the opinion set forth below, I have assumed without verification the genuineness of all signatures, the authenticity of all documents submitted to me as originals, the authenticity of the originals of such documents submitted to me as certified copies, the conformity to originals of all documents submitted to me as copies, the authenticity of the originals of such documents, that all documents submitted to me as certified copies are true and correct copies of such originals and the legal capacity of all individuals executing any of the foregoing documents. In rendering the opinion set forth below, I have also assumed that the Securities will be duly authenticated by the transfer agent and registrar for the Securities.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, I am of the opinion that when the Registration Statement has been declared effective by the SEC and the Securities have been issued, delivered and paid for in the manner contemplated by and upon the terms and conditions set forth in the Registration Statement and the Underwriting Agreement, the Securities will be validly issued, duly authorized, fully paid and nonassessable.

I am a member of the bar of the State of Texas and I do not express any opinion herein concerning any law other than the Texas Business Organizations Code (including the statutory provisions, all applicable provisions of the Texas Constitution and reported judicial decisions interpreting the foregoing).

This opinion letter speaks only as of its date and is delivered in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act. I hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement and to the use of my name under the caption “Legal Matters” in the Prospectus included in the Registration Statement. In giving such consent, I do not hereby admit that I am in the category of persons whose consent is required under Section 7 of the Securities Act, and the rules and regulations of the SEC promulgated thereunder.

Very truly yours,

/s/ Adam D. Nelson