Find a way to do the following card trick. 

In advance, Alice and Bob agree on some protocol. 
Then, the audience chooses 5 arbitrary cards from a standard deck of cards and gives the 5 cards to Alice. 
Alice then shows 4 of the cards, one at a time, to Bob. 
Bob then announces the identity of the 5th card (the one the audience gave to Alice that she did not show to Bob). 
Alice is not allowed to signal Bob in any manner, other than which 4 cards she reveals and the order in which she reveals them.

BONUS: What's the largest size deck of cards (bigger than 52) with which Alice and Bob can do this?