Social Security for Americans Only Act of 2005 - Amends title II (Old Age, Survivors and Disability Insurance) (OASDI) of the Social Security Act (SSA) to: (1) prohibit the wages earned, and self-employment income derived, by individuals who are not citizens or nationals of the United States from being credited for coverage under the OASDI program; and (2) provide the President with authority to enter into agreements with other nations to resolve entitlement and participation questions about their respective social security systems, taking into account such limitation on crediting of wages and self-employment.