There is no single English word that meets the criteria.
relieved
make u fool
r b l j a y c e a
The longest word is 6 letters: rueful
There are 120 ways to order a 5 letter word, however, since there are two "e" letters in the word "green", the number of combinations is only 60.
face paint acquainted availed
feelings
Sized
The word inkiest can be made with those letters.
inertia
If the order matters, i don't know, but if matter doesn't matter you can arrange the letters to get 120 orders.
Refuge