Simplify Tax Filing for Seniors Act of 2005 - Directs the Secretary of the Treasury to make available a new Federal income tax Form 1040S (similar to Form 1040EZ) to individuals who have turned 65 as of the close of the taxable year. Allows the form to be used even if income includes: (1) social security benefits; (2) distributions from qualified retirement plans, annuities, or other such deferred payment arrangements; (3) interest and dividends; or (4) capital gains and losses.