I think you aren't being careful with your signs and
with putting parentheses around what you are substituting.
If your book says the solutions are -5 and -3, then you 
have typed one or two signs wrong in the original problem, 
or else the book has a typographical error, and sometimes 
they do.

You gave the problem as



but the solutions to that are not -5 and -3.

You would have to have had this problem instead

  [not  as the other tutor said.]

In order to get solutions -5 and -3.

Then you would factor and get



and then you'd set each of those = 0 and get

x+5=0      x+3=0
  x=-5       x=-3


But let's suppose it was as you thought

You have this:


x=
x=
x=
x=
x=

Then you'd factor 2 out of the top:

x=

and then cancel the 2's

x=



Edwin