Since both 5n-3 and 3n+7 are equal to m, you can set them equal to each other and just solve from there.
5n-3=3n+7
-3n -3n
2n-3=7
+3 +3
2n=10
————-
2 2
N=5.
Then you can plug it in to check your answer.
5(5)-3 = 22
3(5)+7 =22
They both equal 22 so five is the correct answer.
N=5