(In reply to a start for an analytical solution
by Dej Mar)
I can go further and say that either one of FIVE or TWO must be an odd multiple of 125 and the other is a multiple of 8 and not a multiple of 5.
I concluded this after seeing that the product FIVE*TWO is a multiple of 1000 and the two multiplicands had different ones digits.
Assuming TWO is the multiple of 125 quickly leads to a solution. But that solution has TWO being odd, whereas the problem calls for TWO to be even.