x+y=x-5
I want to get y alone on one side, so if I subtract x from both sides, what would be x - x?
x-x=0, so y = -5
whatever value x has, the equation is still true. You cannot solve for y in terms of x, because y is independent of x in this case.
If you have 3=3, then x+3 = x+3 whatever x is.
Here, y = -5, so x+y = x-5 whatever x is.