Diabetic Foot Complication and Lower Extremity Amputation Reduction Act of 2005 - Amends the Public Health Service Act to direct the Secretary of Health and Human Services to make grants to eligible multidisciplinary health care programs for: (1) providing a high-risk, underserved population with screening, education, and evidence-based medical treatment regarding diabetic foot complications that may lead to lower extremity amputations; and (2) evaluating the quality, cost effectiveness, parity, and patient satisfaction of medical interventions in the prevention of diabetic foot complications and lower extremity amputations.