The correct answer to this 3* 3* 3* 3* 3

The logic being each letter can be mailed through any of the three mails

However I was trying to solve it by making it into an equation

x+y+z=5

we have three mail boxes and total 5 letters

the no of solution to this equation would be

n+r-1Cr

ie 7c2 but then the answer would be wrong.

Why is this logic wrong?