where the first 3 slots are letters and the next 2 are numbers.

There are 26 letters to choose from for the first slot, then 26 for the next (since it doesn't say anything about repeats), then 26, then there are 10 numbers to choose from (0,1,2,3,4,5,6,7,8,9), then 10.

This gives us a total of 26^3 * 10^2 =1757600 different combinations