Health Care Access Assurance Act of 2005 - Requires the Secretary of Health and Human Services to require each State to certify that all State citizens have access to a minimum level of health care coverage as defined by such State. Makes States that are unable to provide such a certification ineligible for funding from the Health Resources and Services Administration (HRSA), the Indian Health Service, the Substance Abuse and Mental Health Services Administration, and the Centers for Medicare & Medicaid Services to support the State's health care system.