Federal Whistleblower Protection Tax Act of 2005 - Amends the Internal Revenue Code to exclude from gross income damages (other than punitive damages and lost income) and amounts awarded as attorney fees and costs for claims under Federal whistleblower provisions prohibiting the discharge of, or discrimination, retaliation, or reprisal against, an employee for asserting rights or taking permitted actions. Provides for the averaging of such lost income for income tax purposes.