We are given 2 points on the line. Equation for the line can be derived, though not necessary here.

1) x > 4
By looking at the graph, we know that whenever x is greater than 4, y is greater than 0.
Hence xy>0
SUFFICIENT

2) -5 < y < 0
As per the graph, This means y is lying in the 4th quadrant.
Therefore x is greater than 0.
y<0, x>0
hence xy<0
SUFFICIENT

However, I have not seen any question where the 2 statements are in conflict with each other.
Statement 1 says xy>0 and statement 2 says xy<0
I am reluctant to choose D
Is this the OA? or am I missing something?

Please find the detailed explanation in the attached jpg file.

You are absolutely right kvcpk. GMAT never gives statements that give conflicting Answers. Therefore I find this question not fit for GMAT. However the same question can be considered for practicing the concepts needed to solve questions that have potential to come in GMAT.

Thanks for all the solutions. I modified this question to get two conflicting answers because I wanted to know what would happen if there were two conflicting statements which are sufficient.

If any instructor can clarify this would be greatly appreciated. Thanks once again!