Answer
$y=-2$
Work Step by Step
A line perpendicular to $x=5$ (a vertical line) is a horizontal line with slope equal to $0$.
Using $y-y_1=m(x-x_1)$ or the Point-Slope Form, the equation of the line with slope $
0
$ and passing through $(
3,-2
)$ is
\begin{array}{l}
y-(-2)=0(x-3)
\\\\
y+2=0
\\\\
y=-2
.\end{array}
