Answer
Both $(5,23)$ and $(-5,0)$ are not solutions.
Work Step by Step
We are given: $5x-y\gt 2 $
Plug in $(-5,0)$:
$5(-5)-0\gt 2 $
$-25 \gt 2 \rightarrow$ false
Plug in $(5,23)$:
$5(5)-23\gt2 $
$2 \lt 2 \rightarrow$ false
Both $(5,23)$ and $(-5,0)$ are not solutions.