This wont work sorry, just like gurmies said
"Your method fails to acknowledge that 135792468 is a possibility...as is something like, say, 821345796"
I might be wrong but:
[4^5 + 3^5 + 2^5 + 1^5]*4! = 31,200
Chose a place for 1, there are 4 spots as you have to allow room for all the...