Exhibit 5.1

GRAUBARD MILLER

THE CHRYSLER BUILDING

405 LEXINGTON AVENUE

NEW YORK, NEW YORK 10174

September 17, 2015                              

Capitol Acquisition Corp. III

509 7th Street, N.W.

Washington, D.C. 20004

Dear Sirs:

Reference is made to the Registration Statement on Form S-1 (“Registration Statement”) filed by Capitol Acquisition Corp. III (“Company”), a Delaware corporation, under the Securities Act of 1933, as amended (“Act”), covering (i) 35,000,000 Units, with each Unit consisting of one share of the Company’s common stock (35,000,000 shares), par value $.0001 per share (the “Common Stock”), and one half of one warrant (17,500,000 warrants) (“Warrants”) each whole Warrant to purchase one share of the Company’s Common Stock (17,500,000 Shares) to Citigroup Global Markets Inc., the representative of the underwriters (the “Underwriters”), (ii) up to 5,250,000 Units (the “Over-Allotment Units”) representing 5,250,000 shares of Common Stock and 2,625,000 whole Warrants (to purchase 2,625,000 shares of Common Stock), which the Underwriters will have a right to purchase from the Company to cover over-allotments, if any, and (iii) all shares of Common Stock and all Warrants issued as part of the Units and Over-Allotment Units.

We have examined such documents and considered such legal matters as we have deemed necessary and relevant as the basis for the opinion set forth below. With respect to such examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as reproduced or certified copies, and the authenticity of the originals of those latter documents. As to questions of fact material to this opinion, we have, to the extent deemed appropriate, relied upon certain representations of certain officers and employees of the Company.

Based upon the foregoing, we are of the opinion that:

1.        The Units, the Over-Allotment Units, the Warrants and the Common Stock to be sold to the Underwriters, when issued and sold in accordance with and in the manner described in the Registration Statement, will be duly authorized, validly issued, fully paid and non assessable.

2.        The Warrants constitute legal, valid and binding obligations of the Company, enforceable against it in accordance with its terms, except (i) as limited by applicable bankruptcy, insolvency, reorganization, moratorium, and other laws of general application affecting enforcement of creditors’ rights generally and (ii) as limited by laws relating to the availability of specific performance, injunctive relief, or other equitable remedies.

We are opining solely on all applicable statutory provisions of Delaware corporate law, including the rules and regulations underlying those provisions, all applicable provisions of the Delaware Constitution and all applicable judicial and regulatory determinations. We hereby consent to the use of this opinion as an exhibit to the Registration Statement, to the use of our name as your counsel and to all references made to us in the Registration Statement and in the Prospectus forming a part thereof. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act, or the rules and regulations promulgated thereunder.

Very truly yours,

/s/ Graubard Miller