First, we distribute the 2 through the parenthesis.
3x+2x+8=5(x+1)+3
Then we distribute the 5 through the parenthesis
3x+2x+8=5x+5+3
Collect the like terms
5x+8=5x+5+3
Add the numbers
5x+8=5x+8
The statement is true for any value of x, because both sides are identical