Federal Pell Grant Eligibility Clarification Act of 2005 - Amends the Higher Education Act of 1965 to revise eligibility requirements for certain Pell Grant awards by modifying the formula for determining total income to include consideration of current year circumstances for students residing in states in which an extended benefit period under the Federal-State Extended Unemployment Compensation Act of 1970 is in effect, or would be effect if a specified circumstance applied.