Student Aid Reward Act of 2005

Student Aid Reward Act of 2005 - Amends the Higher Education Act of 1965 (HEA) title IV (Student Assistance) to direct the Secretary of Education to carry out a Student Aid Reward (SAR) Program of payments to institutions of higher education (IHEs) to encourage them to participate in the student loan program under title IV that is most cost-effective for taxpayers.

Requires that a SAR payment to an IHE equal at least 50 percent of the savings to the Federal Government generated by the IHE's participation in the most cost-effective student loan program, rather than one not cost-effective for taxpayers.

Requires IHEs receiving SAR payments to: (1) provide student loans under that most cost-effective program for five years after the payment date; and (2) use payment funds, where appropriate, to supplement students Pell Grants. Allows such funds to be used also to award need-based grants to lower and middle income graduate students.