You pull up today$$s Wordle, which is a game where you guess a $5-$letter word chosen by

the game. In Wordle, each letter of the guess is colored by the following rules:

$$ green means that the letter you guessed appears in the word and in the right place,

$$ gray means your letter does not appear in the word anywhere.

$$ yellow means your letter appears in the word somewhere, but not in the correct place.

For example, if the hidden game word is $$HARPY$$ and you guessed $$LASER$,$ then $$A$$

would be colored green, $$L$,$S$,$E$,$ would be colored gray, and $$R$$ would be colored

yellow.

You guess $$ARISE$.$ The game colors the letter S green and all the other letters gray.

Given this information, how many $5-$letter words are possible? $($for this question, ignore

whether a word is an actual English word; for example, $$XXFSV$$ would also satisfy the

problem.$)$