SPONSOR WARRANT EXCHANGE LETTER AGREEMENT

Exhibit 10.5

SPONSOR WARRANT EXCHANGE LETTER AGREEMENT

September 21, 2014

Hennessy Capital Acquisition Corp.

700 Louisiana Street, Suite 900

Houston, Texas 77002

The Traxis Group B.V.

c/o Cerberus Capital Management L.P.

875 Third Avenue

New York, NY 10022

Gentlemen:

Reference is made to that certain purchase agreement by and between Hennessy Capital Acquisition Corp. (the “Company”) and The Traxis Group, B.V. (“Traxis), dated as of the date hereof (the “Purchase Agreement”). In order to induce Traxis to enter into the Purchase Agreement, Hennessy Capital Partners I LLC (“HCPI”) has agreed to enter into this letter agreement (this “Agreement”) relating to the exchange of a number of warrants sold to HCPI by the Company in a private placement in connection with the Company’s initial public offering (the “Private Placement Warrants”) equal to (i) 12,125,000 less (ii) the number of public warrants validly tendered and not withdrawn in the Warrant Exchange Offer for shares of common stock (“Common Stock”) of the Company. For purposes of this letter, the term “Exchange Private Placement Warrants” shall refer solely to the Private Placement Warrants to be exchanged pursuant to the immediately preceding sentence and “Exchange Shares” shall refer to any shares of Common Stock of the Company to be issued to HCPI pursuant to this Agreement. Capitalized terms used and not otherwise defined herein are defined in the Purchase Agreement and shall have the meanings given to such terms in the Purchase Agreement.

HCPI and the Company hereby agree with Traxis as follows:

1. If the Warrant Exchange Offer is consummated prior to the Closing Date, then at the Closing HCPI shall exchange each Exchange Private Placement Warrant for 0.10 shares of Common Stock, resulting in the issuance to HCPI of up to 1,212,500 shares of Common Stock. In order to effectuate such exchange, upon the Closing, HCPI shall deliver its original Private Placement Warrants to the Company against delivery of a stock certificate for the Exchange Shares and the Company shall return to HCPI a replacement Private Placement Warrant representing the difference, if any, between the 12,125,000 Private Placement Warrants initially issued to HCPI and the number of Exchange Private Placement Warrants to be exchanged pursuant to this paragraph 1. The Company agrees that the registration rights granted to HCPI with respect to the Exchange Private Placement Warrants shall continue with respect to the Exchange Shares to be issued to HCPI hereunder.

2. If, however, the Warrant Exchange Offer has not been consummated prior to the Closing Date, then the following shall occur:

a. At the Closing, HCPI shall deliver to the Company its original Private Placement Warrants. Each of 6,375,000 of such Private Placement Warrants shall be exchanged at the Closing for 0.10 shares of Common Stock, resulting in the issuance to HCPI of 637,500 shares of Common Stock.

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b. In addition, if the Warrant Exchange Offer is consummated during the period commencing on the Closing Date and ending on the 15th calendar day following the Closing Date (such date of consummation, if any, the “Post-Closing Warrant Exchange Offer Closing Date” and such 15th calendar day, the “Outside Date”), then the Company (and HCPI, if so directed by the Company) shall direct the Company’s transfer agent (or such other intermediaries as appropriate) to take such actions, and HCPI shall take such actions, as are necessary to cause the exchange by HCPI of, and HCPI shall so exchange, an additional amount of Private Placement Warrants equal to (i) 5,750,000 less (ii) the number of public warrants validly tendered and not withdrawn in the Warrant Exchange Offer for 0.10 shares of Common Stock, resulting in the issuance to HCPI of up to an additional 575,00 shares of Common Stock. In order to effectuate such exchange on the Post-Closing Warrant Exchange Offer Closing Date, if any, the Company shall return to HCPI a replacement Private Placement Warrant representing the difference, if any, between the 12,125,000 Private Placement Warrants initially issued to HCPI and the total number of Exchange Private Placement Warrants exchanged pursuant to paragraphs 2(a) and 2(b) of this Agreement; provided, however, that, notwithstanding anything to the contrary in this paragraph 2(b), if the Warrant Exchange Offer has not been consummated on or prior to the Outside Date, then the Company (and HCPI, if so directed by the Company) shall direct the transfer agent (or such other intermediaries as appropriate) to take such actions, and HCPI shall take such actions, as are necessary to cause the exchange by HCPI of, and HCPI shall so exchange, all outstanding Private Placement Warrants on the Business Day immediately following the Outside Date, for 0.10 shares of Common Stock, resulting in the issuance to HCPI of an additional 575,000 shares of Common Stock.

3. In furtherance, and not in limitation of, any other restrictions applicable to the Private Placement Warrants, whether pursuant to the terms of any such Private Placement Warrant or otherwise, no Private Placement Warrants shall be exercised by HCPI prior to the second Business Day following the Outside Date.

4. From the Closing Date until the earliest of: (a) the 180th day after the Closing Date, (b) the date following the Closing Date on which the Company completes a liquidation, merger, stock exchange or other similar transaction that results in all of the Company’s stockholders having the right to exchange their shares of Common Stock for cash, securities or other property and (c) if the last sale price of the Company’s common stock equals or exceeds $12.00 per share (as adjusted for stock splits, stocks dividends, reorganizations, recapitalizations and the like) for any 20 trading days within any 30-trading day period commencing at least 150 days after the Business Combination, the close of business on such 20th trading day ( such 20^th trading day, the “Alternative Lock-up Termination Date”) (the period from the Closing Date until the earliest of clause (a), (b) and (c), the “Lock-Up Period”), it will not: (i) sell, offer to sell, contract or agree to sell, hypothecate, pledge, grant any option to purchase or otherwise dispose of or agree to dispose of, directly or indirectly, or establish or increase a put equivalent position or liquidate or decrease a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended, and the rules and regulations of the Securities and Exchange Commission promulgated thereunder, with respect to the Exchange Shares , any shares of Common Stock issuable pursuant to those Private Placement Warrants that do not constitute Exchange Private Placement Warrants or the Founder Earnout Shares (as defined in the letter agreement, dated January 16, 2014, between HCPI and the Company), (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of any of the Exchange Shares , any shares of Common Stock issuable pursuant to those Private Placement Warrants that do not constitute Exchange Private Placement Warrants or the Founder Earnout Shares, in cash or otherwise, or (iii) publicly announce any intention to effect any transaction specified in clause (i) or (ii).

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5. The undersigned hereby authorizes the Company during the Lock-Up Period to cause its transfer agent for the Exchange Shares , any shares of Common Stock issuable pursuant to those Private Placement Warrants that do not constitute Exchange Private Placement Warrants and the Founder Earnout Shares to decline to transfer, and to note stop transfer restrictions on the stock register and other records relating to, the Exchange Shares , any shares of Common Stock issuable pursuant to those Private Placement Warrants that do not constitute Exchange Private Placement Warrants and the Founder Earnout Shares for which the undersigned is the record holder and, in the case of the Exchange Shares , any shares of Common Stock issuable pursuant to those Private Placement Warrants that do not constitute Exchange Private Placement Warrants and the Founder Earnout Shares for which the undersigned is the beneficial but not the record holder, agrees during the Lock-Up Period to cause the record holder to cause the relevant transfer agent to decline to transfer, and to note stop transfer restrictions on the stock register and other records relating to, such Exchange Shares , any shares of Common Stock issuable pursuant to those Private Placement Warrants that do not constitute Exchange Private Placement Warrants and the Founder Earnout Shares, if such transfer would constitute a violation or breach of this Agreement.

6. Notwithstanding the foregoing, HCPI may sell or otherwise transfer all or a portion of the Exchange Shares, any shares of Common Stock issuable pursuant to those Private Placement Warrants that do not constitute Exchange Private Placement Warrants or the Founder Earnout Shares to: (i) its direct or indirect equity holders or to any of its other affiliates (as defined in Regulation C of the Securities Act of 1933, as amended), (ii) the immediate family members (including spouses, significant others, lineal descendants, brothers and sisters) of its direct or indirect equity holders or any of its other affiliates, (iii) a family trust, foundation or partnership established for the exclusive benefit of HCPI, its direct or indirect equity holders, any of its affiliates or any of their respective immediate family members or (iv) a charitable foundation controlled by HCPI, its direct or indirect equity holders, any of its affiliates or any of their respective immediate family members, provided in each such case that the transferee thereof enters into a written agreement to be bound by the restrictions set forth herein.

7. This Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any way to the subject matter hereof. This Agreement may not be changed, amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument executed by all parties hereto.

8. No party hereto may assign either this Agreement or any of its rights, interests, or obligations hereunder without the prior written consent of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate to transfer or assign any interest or title to the purported assignee. This Agreement shall be binding on the undersigned and their respective successors and assigns.

9. This Agreement shall be governed by and construed and enforced in accordance with the laws of the State of Delaware, without giving effect to conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The parties hereto (i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Agreement shall be brought and enforced in the Court of Chancery of the State of Delaware (or, if the Court of Chancery of the State of Delaware lacks jurisdiction, then in the applicable Delaware state court), or if under applicable Law exclusive jurisdiction of such action is vested in the federal courts, then the United States District Court for the District of Delaware, and irrevocably submits to such jurisdiction and venue, which jurisdiction and venue shall be

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exclusive, and (ii) waives any objection to such exclusive jurisdiction and venue or that such courts represent an inconvenient forum.

10. Any notice, consent or request to be given in connection with any of the terms or provisions of this Agreement shall be in writing and shall be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery or facsimile transmission.

11. This agreement shall terminate at such time, if any, that the Purchase Agreement is terminated in accordance with its terms.

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Please indicate your agreement to the foregoing by signing in the space provided below.

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