Answer :

5n + 10 = 6n + 3
10 – 3 = 6n – 5n
7 = 1n
n = 7

Nothing else to add, I think it's complete. If anything else you don't understand, or want to make something clearer, message me.

Here is another way to look at it:
1. 5(n+2)=3/5(5+10n)
2. Do foil >> 5n+10=3+6n
3. Subtract "3" from each side >> 5n+7=6n
4. Isolate "n" and subtract "5n" from each side >> 7=n


  5n + 10 = ³/₅(5 + 10n)
  5n + 10 = ³/₅(5) + ³/₅(10n)
  5n + 10 = 3 + 6n
- 5n                - 5n
          10 = 3 + n
          - 3 - 3       
            n = 7