Material Support to Terrorism Prohibition Improvements Act of 2005 - Repeals a sunset provision in the Intelligence Reform and Terrorism Prevention Act of 2004 concerning material support of terrorism.

Amends the Immigration and Nationality Act (INA) to expand the definition of alien terrorists deemed inadmissible to include persons who: (1) engage in specified terrorist-related activities regardless of whether they are affiliated with a designated foreign terrorist organization; or (2) have received military-type training from an organization that was a terrorist organization at the time of training. Makes persons who receive such military-type training subject to removal to the same degree that they would be inadmissible.

States that this Act's amendments to the INA shall apply to: (1) all aliens subject to removal, deportation, or exclusion at any time; and (2) acts and conditions constituting grounds for inadmissibility, exclusion, deportation, or removal occurring or existing before, on, or after the date of enactment.

Amends the Federal criminal code to increase penalties and establish mandatory minimum sentences for providing material support to terrorists or designated foreign terrorist organizations and for receiving military-type training from a foreign terrorist organization.