Controlled Substances Export Reform Act of 2005 - Amends the Controlled Substances Import and Export Act to authorize the Attorney General to allow any controlled substance that is in schedule I or II, or that is a narcotic drug in schedule III or IV, to be exported from the United States to a country (first country) for subsequent export to another country (second country) if: (1) both such countries are parties to the Single Convention on Narcotic Drugs, 1961, and the Convention on Psychotropic Substances, 1971; (2) each of such countries has maintained an adequate system of substance import controls; (3) the substance is consigned to a holder of permits or licenses required under the first country's laws and a permit to import the substance has been issued; (4) substantial evidence that the substance is to be consigned to a permit holder as required under the second country's laws is furnished, a permit to import it is to be issued, the substance is to be applied exclusively to legitimate uses within that country, and it will not be re-exported; (5) within 30 days after export from the first country, the person who exported it from the United States certifies that re-export has occurred; and (6) the Attorney General has issued a permit to export the substance from the United States.