Fair Care for the Uninsured Act of 2005

Fair Care for the Uninsured Act of 2005 - Amends the Internal Revenue Code to allow a refundable tax credit for health insurance paid for the benefit of a taxpayer, his spouse, and dependents (no more than two). Directs the Secretary of the Treasury to make advance payments of credit amounts to the provider of the taxpayer's health insurance.

Requires each health insurer, health maintenance organization, and health service organization to participate in a State-established health insurance safety net to assure the availability of health insurance to uninsurable individuals. Funds such safety nets through assessments against such insurers and organizations. Permits such insurers and organizations to add the costs of such assessments to the costs of their insurance or coverage.

Amends the Public Health Service Act to allow health benefits coverage through individual membership associations (IMAs). Sets forth IMA requirements, including that the IMA be an organization operated under the direction of an association and that IMA health benefits coverage only be provided through contracts with health insurance issuers. Requires IMAs to include a minimum of two health insurance coverage options.