I'll walk you through your reasoning. I think you're not necessarily wrong here - but you've gone too far on a data sufficiency problem in the "what might be the case" scenarios, which isn't really an efficient use of your time here.
to set the equation on the right to zero, x= -5 OR y = 5
* X can be -5. If X = -5 then the right side of the equation is 0, but X^2 must equal Y^2.
so this means while X = -5, Y can be either 5 or -5 and equations on the left and right would = 0. Correct?
Yes -- IF x is -5, AND y is either 5 or -5, THEN the equation works. If this isn't the case, though, the equation doesn't work. Since we don't know whether this very specific case is the scenario, we don't have enough information. Basically, we have 1 equation and 2 unknowns, so we have insufficient information.
* Y can be 5. If Y = 5, then the right side of the equation is 0, but X^2 must equal Y^2 to make the left side of the equation = 0.
so this means while Y= 5, X can be either 5 or -5. correct?
Same issue here -- You've presented one other scenario where we MIGHT have a situation that makes the equation work, but we don't have any information that leads us to believe that this might actually be the case.
Thus, your reasoning is sound, but unnecessary in this situation.
Hope this helps,