Border Law Enforcement Relief Act of 2005 - Authorizes the Secretary of Homeland Security to award grants to a tribal, state, or local law enforcement agency located in a county within 100 miles of a U.S. border with Canada or Mexico, or in a county beyond 100 miles that has been certified by the Secretary as a high impact area, to provide assistance in addressing: (1) criminal activity that occurs by virtue of proximity to the border; and (2) the U.S. government's failure to adequately secure its borders. Directs the Comptroller General to report to Congress on the costs incurred by law enforcement agencies in connection with such criminal activity or failure.