Federal Aviation Safety Security Act of 2005 - Declares that functions performed by air traffic control specialists at Federal Aviation Administration flight service stations are inherently governmental functions, and must be performed by Federal employees. Voids any action taken pursuant to the Federal Activities Inventory Reform Act of 1998 to include such functions on certain annual Federal agency lists (submitted to the Office of Management and Budget) of government activities performed by Federal Government sources for an agency that are not inherently governmental functions.