Question 147378
Assuming the first two keys are digits and the last three are letters (that is, assuming we know in advance this is that case), then

The first key is digits - so Alan has 10 choices
The second key is digits, but can't be the same digit used on key 1. So 10-1=9
The third key is letters - 26 possibilities
The fourth key is letters - 26 possibilities
The fifth key is letters - 26 possibilities

So, 10*9*26*26*26 possible permutations

I never thought I would see a mathematics problem that appeals to a thief!

Next question, what is the probability Alan gets caught and goes to jail? :)