MATH problem?

Question

xxx
*xx
= xxxx
+xxxx0
=xxxxx

Using only 2,3,5,7 what is the final answer

Answer 1

... 775
.x...33
---------
..2325
2325
---------
25575

Some things to realize:
2 can't be the last digit because multiplying will result in an even number.

3 can't be the last digit unless it is paired with 5.
7 can't be the last digit unless it is paired with 5.
5 can pair with anything except 2.

So obviously we need a multiple of 5 at the top. I created a list of 3 digit combinations that end it 3, 5 or 7. The first digit can't be too small or else you won't get to a four digit number when you multiply.

Anyway, a little trial and error and a spreadsheet and I came up with the answer above.