The first letter can be any one of 8. For each of those . . .
The second letter can be any one of the remaining 7. For each of those . . .
The third letter can be any one of the remaining 6. For each of those . . .
The fourth letter can be any one of the remaining 5. For each of those . . .
The fifth letter can be any one of the remaining 4.
The total number of possibilities is (8 x 7 x 6 x 5 x 4) = 6,720 .
(That's 8! / 3! .)
Note:
If you're allowed to use the same letter more than once,
then there are 8 choices for each of the 5 letters.
The total number of possibilities then is (8 x 8 x 8 x 8 x 8) = 32,768 .
(That's 8⁵ or 2¹⁵ .)