Earned Income Tax Credit Simplification Act of 2005 - Amends provisions of the Internal Revenue Code relating to the earned income tax credit to: (1) allow certain married taxpayers filing separate returns and residing with a dependent child to claim such credit; (2) allow certain taxpayers residing in a household with a qualifying child to claim the credit independently as a taxpayer without a qualifying child; (3) eliminate provisions denying the credit for individuals with excessive investment income; and (4) require aliens claiming the credit to have a social security number authorized for employment purposes.