No Social Security for Illegal Immigrants Act of 2005 - Amends title II (Old Age, Survivors and Disability Insurance) (OASDI) of the Social Security Act to exclude from creditable wages and self-employment income any wages earned for services by aliens performed in the United States, and self-employment income derived from a trade or business conducted in the United States, while the alien was not authorized to be so employed or to perform a function or service in such a trade or business.