The first letter can be any one of the 26 in the alphabet.
For each one ...
The 2nd letter can be any one of the remaining 25.
For each one ...
The 3rd letter can be any one of the remaining 24.
For each one ...
The 4th letter can be any one of the remaining 23.
For each one ...
The 5th letter can be any one of the remaining 22.
The total number of possibilities is
(26 · 25 · 24 · 23 · 22) = 7,893,600 .
