Answer
$(0,0)$ is not a solution of the inequality.
Work Step by Step
The given inequality is
$\Rightarrow 4x-y\geq 5$
Substitute $0$ for $x$ and $0$ for $y$.
$\Rightarrow 4(0)-(0)\geq 5$
Simplify.
$\Rightarrow 0-0\geq 5$
$\Rightarrow 0\geq 5$
False.
Hence, $(0,0)$ is not a solution of the inequality.