Children's Hope Act of 2005 - Amends the Internal Revenue Code to allow a tax credit, up to $100 ($200 for joint returns), for charitable contributions to an education investment organization that disburses 90% of its contributions to provide grants to students for elementary and secondary education expenses, if at least 50% of such disbursements go to students who qualify for free or reduced-cost school lunches. Requires a taxpayer claiming such credit to first claim a state qualified scholarship tax credit, as defined by this Act, as a condition of eligibility for the federal tax credit.