Trail of the Ancients National Heritage Area Study Act of 2005 - Directs the Secretary of the Interior, in cooperation with the Four Corners Heritage Council, to conduct a study to assess the feasibility and suitability of designating the Four Corners region comprised of parts of San Juan County, Utah, Montezuma and Dolores Counties, Colorado, Apache and Navajo Counties, Arizona, and San Juan and McKinley Counties, New Mexico, and parts of the reservations of the Ute Mountain Ute, Navajo, and Hopi Tribes in those States as the "Trail of the Ancients National Heritage Area."