13D Filing: Sessa Capital (master) Files Grievance With NYSE Over Ashford Hospitality Prime, Inc. (AHP)’s Penny Preferred Stock Issuance

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

Schedule 13D

Under the Securities Exchange Act of 1934

(Amendment No. 5)*

Ashford
Hospitality Prime, Inc.

(Name of Issuer)

Common Stock, $0.01 par value per share

(Title of Class of Securities)

044102101

(CUSIP Number)

Thomas R. Stephens

Bartlit Beck Herman Palenchar & Scott LLP

1899 Wynkoop Street, Suite 800

Denver, Colorado 80202

(303) 592-3100

(Name,
Address and Telephone Number of Person Authorized to Receive Notices and Communications)

February 17, 2016

(Date of Event which Requires Filing of this Statement)

If the filing person has
previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§ 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following
box.  ¨

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See Rule 13d-7 for
other parties to whom copies are to be sent.

*	The remainder of this cover page shall be filled out for a reporting persons initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be
deemed to be filed for the purpose of Section 18 of the Securities Exchange Act of 1934 (Act) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act
(however, see the Notes).

(Continued on following pages)