The 5th and the 14th amendment cover all people, not just citizens.
Here is an informative read on how and why and the history of the question of non-citizen rights.
http://scholarship.law.georgetown.edu/cgi/viewcontent.cgi?ar...
Found this after a discussion of the rights of Boston Marathon suspects as non-citizens. Pretty much they have every right of a non-citizen, except the right to vote.