National Historic Preservation Act Amendments of 2005 - Amends the National Historic Preservation Act (NHPA) to: (1) continue providing for the coverage of funds into the Historic Preservation Fund through FY2011 pursuant to such Act; (2) modify membership and quorum requirements for the Advisory Council on Historic Preservation; (2) allow agencies or private entities, other than the Department of the Interior, to provide financial and administrative services to the Council by agreement; (3) authorize the Council to enter into cooperative agreements with any Federal agency that administers an NHPA grant or assistance program to improve program administration; and (4) authorize the Council to evaluate the effectiveness of such programs and make recommendations for improvement to agency heads, the President, and Congress.