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I would pick B. I hope I'm not forgetting some number property here.

Statement 1 is not sufficient. 1. x > y+5

x could be 7 and y could be 1, giving you 7>6, which will give you a 7>36 when values are replaced in the stem, therefore gives you a NO answer, but when x is 200 it gives you a YES answer.

Statement 2 is sufficient. x^2 - y^2 = 0

This could be x=5 or -5, y=5 or -5, giving you 25-25=0, which gives you a NO answer, but what if x=1 or -1, and y=1 or -1? answer would still be NO.

As explained by others, both of them alone is insufficient.
Lets see what they make together:

according to (2): x = y
applying in (1) makes: x > x+5
that can never be true and therefore does not give any further information to reach a decision if x > y^2 or not.