Answer
$r \cos (\theta -\dfrac{\pi}{2})=-5$
Work Step by Step
Conversion of polar coordinates and Cartesian coordinates are as follows:
a)$r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$
b) $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
c) $x=r \cos \theta$
d) $y=r \sin \theta$
We are given that $y=-5$
This implies that $r \sin \theta=-5$
or, $r \cos (\dfrac{\pi}{2}-\theta)=-5$
Thus, $r \cos (\theta -\dfrac{\pi}{2})=-5$
