Question

How many 5-letter passwords can be created if no letter can be used twice within the password?

Answer 1

If there are 5 letters used only, then 5! or 5*4*3*2 = 120
If all 26 letters of the alphabet may be used for the code, then:
26*25*24*23*22
If you mean letters of the alphabet, and not case sensitive, it's26*25*24*23*22
= 7893600

Answer 2

26*25*24*23*22=7893600

or you can use

26!/(26-5)!=7893600