Kidney Patient More Frequent Dialysis Quality Act of 2005 - Amends title XVIII (Medicare) of the Social Security Act to direct the Secretary of Health and Human Services to publish final regulations for equivalent per treatment prospective payment rates for more frequent hemodialysis treatments furnished to qualified individuals at home and in a facility (commonly known as composite Method I and Method II Cap rates), and prospective payment rates for in-facility training for more frequent hemodialysis.