Veterans Self-Employment Act of 2005 - Directs the Secretary of Veterans Affairs to conduct a five-year pilot project to test the feasibility and advisability of the use of educational assistance under certain programs of the Department of Veterans Affairs to pay for training costs associated with the purchase of a franchise enterprise. Prohibits the use of such assistance unless: (1) training is required and provided in connection with the purchase and operation of a franchise; and (2) such training, and the training entity, are approved by the Secretary. Provides training and entity approval requirements.