Exhibit 10.5

SECOND AMENDMENT

TO PIPELINES AND TERMINALS AGREEMENT

This Second Amendment (the “Second Amendment”) to the Pipelines and Terminals Agreement dated February 28, 2005 (the “Original Agreement”), by and between Holly Energy Partners, L.P. (“HEP”) and Alon USA, L.P. (“ALON”) (collectively, the “Parties”), is entered into as of the             day of             , 2011 (the “Effective Date”).

WHEREAS, the Original Agreement has been previously amended by a Letter Agreement dated January 25, 2005, a Second Letter Agreement dated June 29, 2007, and a First Amendment of Pipelines and Terminals Agreement dated effective September 1, 2008 (the Original Agreement, as amended to the date hereof, being referred to herein as the “Agreement”); and

WHEREAS, ALON, as agent for J. Aron & Company (“J. Aron”), desires to utilize ALON’s rights under the Agreement to transport and store, and obtain handling services for, product owned by J. Aron.

NOW, THEREFORE, the Parties and J. Aron agree to add the following terms as Section 22 to the Agreement:

SECTION 22

(a) J. Aron Product. From time to time during the term of the Agreement, ALON may designate in writing to HEP that all of the products being stored and handled by HEP pursuant to the Agreement are owned by J. Aron (the “J. Aron Product”), other than ethanol and additives. Upon receipt of such written designation, HEP shall note in its records and account for separately the J. Aron ownership until such time as J. Aron notifies HEP in writing that ownership in such product has been transferred from J. Aron to ALON, it being the intention that HEP shall not be required to recognize any other transfers of ownership of any stored product (other than transfers from J. Aron to ALON) unless such transfer and recognition are agreed to in writing by HEP in its sole discretion. ALON shall act as J. Aron’s sole agent for all purposes of the Agreement, and, subject to paragraph 22(b) below, HEP shall be entitled to follow ALON’s instructions with respect to all J. Aron Product that is transported, stored or handled by HEP pursuant to the Agreement. For avoidance of doubt, specifically, without limitation, but subject to paragraph 22(b) below, HEP shall have the right to transfer possession of J. Aron Product to ALON’s customers or otherwise as instructed by ALON.

(b) J. Aron Instructions. Notwithstanding the agency provisions of paragraph 22(a) above, at any time HEP has possession of any J. Aron Product under this Agreement, J. Aron shall have the right to either (i) deliver to HEP a written notice instructing HEP to promptly within a reasonable time stop all transfers of J. Aron Product into and out of HEP’s pipeline and storage system covered by this Agreement (the “Covered System”), and thereafter to promptly within a reasonable time evacuate all J. Aron Product then being held by HEP out of the Covered System to a destination listed by J. Aron in the written notice, or (ii) deliver to HEP a written notice instructing HEP to accept further transfers of J. Aron Product into the Covered System for

a period of fourteen days (solely to allow J. Aron to transport product owned by J. Aron and located at ALON’s Big Springs, Texas, refinery), and to promptly within a reasonable time evacuate all J. Aron Product out of the Covered System to a destination listed by J. Aron in the written notice, in each case pursuant to terms and conditions identical to those set forth in this Agreement. Upon receipt of instructions from J. Aron as described in clause (i) or (ii) of the preceding sentence, HEP will cease taking instructions from ALON with respect to J. Aron Product and will follow the written instructions received from J. Aron pursuant to clause (i) or (ii) of the preceding sentence. Upon issuance of instructions as described in clause (i) or (ii) above, J. Aron will be liable to HEP for all costs under this Agreement with respect to J. Aron Product as well as all incremental or additional costs of complying with the instructions sent by J. Aron under clause (i) or (ii) above. After J. Aron delivers to HEP instructions as described in clause (i) or (ii) above, J. Aron may request that HEP engage in discussions regarding other instructions with respect to J. Aron Product, but HEP shall have no obligation to follow or recognize such other instructions unless such other instructions are agreed to by HEP and documented to HEP’s satisfaction, in each case in HEP’s sole discretion.

(c) Pro Rata Treatment. All J. Aron Product shall be subject to pro rata treatment pursuant to the Agreement with respect to matters related to shortages and overages of quantity, specifications, and dealing with trans-mix.

(d) Product Measurements; Inventory Reports; Notices. ALON and J. Aron shall each have the product measurement rights provided for in Section 8 of this Agreement for so long as any J. Aron Product is located in the Refined Product Pipelines or Refined Product Terminals. HEP shall send the inventory reports described in Section 8 of this Agreement and notices delivered pursuant to Section 20 of this Agreement to J. Aron at the following address, with copies to ALON:

(d) All Provisions in Effect. All provisions of the Agreement, as amended or adjusted by this Section 22, shall be in full force and effect with respect to J. Aron Product as if the J. Aron Product was owned by ALON.

(d) Payment by ALON. Except as set forth in Section 22(b) above, ALON shall be solely liable under this Agreement for all amounts owed to HEP under this Agreement with respect to J. Aron Product. Any failure to timely pay any such amounts shall be deemed a default under this Agreement, and HEP shall be entitled to enforce all of its remedies with respect to such default as set forth in this Agreement or otherwise available at law or in equity.

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This Second Amendment has been executed as of the date first above written.

J. Aron hereby agrees to be bound by this Second Amendment and such portions of the Agreement that apply to J. Aron or J. Aron Product.

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