Answer
$r=\frac{5}{\cos\theta-\sin\theta}$.
Work Step by Step
To convert from polar to rectangular coordinates we use $x=r\cos\theta$ and $y=r\sin\theta$. To convert from rectangular to polar coordinates, we use $r=\pm\sqrt{x^2+y^2}$, $\tan\theta=\frac{y}{x}$, but aware of which quadrant the point lies in.
Hence here $x-y=5\\r\cos\theta-r\sin\theta=5\\r(\cos\theta-\sin\theta)=5\\r=\frac{5}{\cos\theta-\sin\theta}$.