Exhibit 99.5

THIS PROXY CARD IS VALID ONLY WHEN SIGNED AND DATED. KEEP THIS PORTION FOR YOUR RECORDS DETACH AND RETURN THIS PORTION ONLY TO VOTE, MARK BLOCKS BELOW IN BLUE OR BLACK INK AS FOLLOWS: Signature [PLEASE SIGN WITHIN BOX] Date Signature (Joint Owners) Date 0 0 0 0 0 0 0 0 0 0 0 00001090551 R1.0.0.11699 HOLLY CORPORATION ATTN: LEGAL DEPARTMENT 100 CRESCENT COURT SUITE 1600 DALLAS, TX 75201-6915 VOTE BY INTERNET — www.proxyvote.com Use the Internet to transmit your voting instructions and for electronic delivery of information up until 11:59 P.M., eastern time, on June 27, 2011. Have your proxy card in hand when you access the web site and follow the instructions to obtain your records and to create an electronic voting instruction form. Do not mail back the below proxy card. VOTE BY PHONE — 1-800-690-6903 Use any touch-tone telephone to transmit your voting instructions up until 11:59 P.M., eastern time, on June 27, 2011. Have your proxy card in hand when you call and then follow the instructions. Do not mail back the below proxy card. VOTE BY MAIL Mark, sign and date your proxy card and return it in the postage-paid envelope we have provided or return it to Vote Processing, c/o Broadridge, 51 Mercedes Way, Edgewood, NY 11717. The Board of Directors recommends you vote FOR proposals 1, 2 and 3. For Against Abstain 1 To approve the issuance of shares of Holly Corporation (Holly) common stock, par value $0.01 per share, to Frontier Oil Corporation (Frontier) shareholders in connection with the merger contemplated by the Agreement and Plan of Merger,dated February 21, 2011, by and among Holly, Frontier and North Acquisition, Inc., as it may be amended from time to time. 2 To approve and adopt Holly’s amended and restated certificate of incorporation to, among other things, (i) increase the number of authorized shares of Holly capital stock from 161 million to 325 million shares and (ii) change the name of Holly to HollyFrontier Corporation. 3 To approve the adjournment of the Holly special meeting to a later date or dates, if necessary or appropriate, to solicit additional proxies in the event there are not sufficient votes at the time of the special meeting to approve the first proposal listed above. NOTE: Such other business as may properly come before the Meeting or any adjournment or postponement thereof. Please sign exactly as your name(s) appear(s) hereon. When signing as attorney, executor, administrator, or other fiduciary, please give full title as such. Joint owners should each sign personally. All holders must sign. If a corporation or partnership, please sign in full corporate or partnership name, by authorized officer. Yes No Please indicate if you plan to attend this meeting 00001090552 R1.0.0.11699

Important Notice Regarding the Availability of Proxy Materials for the Special Meeting: The Notice of Special Meeting Of Stockholders and Proxy Statement is/are available at www.proxyvote.com . HOLLY CORPORATION Special Meeting of Stockholders June 28, 2011 This proxy is solicited by the Board of Directors The undersigned hereby appoint(s) Matthew P. Clifton, Bruce R. Shaw and Denise C. McWatters, or any of them, as proxies, each with the power to appoint his/her substitute, and hereby authorizes them to represent and to vote, as designated on the reverse side of this ballot, all of the shares of common stock of Holly Corporation that the undersigned is/are entitled to vote at the special meeting of stockholders to be held at 3:00 PM CDT on June 28, 2011 at The Crescent Club, 200 Crescent Court, 17th Floor, Dallas, Texas 75201, and any adjournment or postponement thereof. This proxy, when properly executed, will be voted in the manner directed herein. In the absence of specific direction, signed proxies will be voted in accordance with the recommendations of the Board of Directors. Continued and to be signed on reverse side