simplify x-3/3 - x-2/5
5(x-3) - 3(x-2)/15
5x-15 - 3x+6/15
is it :2x-21/15???
Your lack of brackets make the order of operation incorrect.
Here is probably what you meant
(x-3)/3 - (x-2)/5
=(5(x-3) - 3(x-2))/15
= (5x-15 - 3x+6)/15
= (2x - 9)/15
notice your constant in the last line is incorrect