The polar coordinates and the cartesian coordinates are related by the following relation
[tex]\begin{cases}x=r\cos \theta \\ y=r\sin \theta\end{cases}[/tex]
We just need to substitute our values on this expression, and evaluate to find our coordinates on rectangular coordinates.
[tex]\begin{gathered} (r,\theta)=(-5,\frac{3\pi}{2}) \\ \Rightarrow\begin{cases}x=-5\cos \frac{3\pi}{2} \\ y=-5\sin \frac{3\pi}{2}\end{cases} \end{gathered}[/tex]
Those trigonometric functions have known values
[tex]\begin{gathered} \cos \frac{3\pi}{2}=0 \\ \sin \frac{3\pi}{2}=-1 \end{gathered}[/tex]
Plugging those values in our expression, we have
[tex]\begin{cases}x=-5\cdot(0) \\ y=-5\cdot(-1)\end{cases}\Rightarrow\begin{cases}x=0 \\ y=5\end{cases}[/tex]
Our point written in rectangular coordinates is
[tex](0,5)[/tex]
