Chisholm and Great Western Cattle Trails Act of 2005 - Amends the National Trails System Act to direct the Secretary of the Interior to conduct separate studies to determine the feasibility and suitability of designation of: (1) at least one of the routes commonly known as the Chisholm Trail as components of the Chisholm Trail National Historic Trail; and (2) at least one of the routes commonly known as the Great Western Trail as components of the Great Western Trail National Historic Trail.