Answer
$\left( {5,\frac{{3\pi }}{2}} \right),\left( { - 5,\frac{\pi }{2}} \right)$
Work Step by Step
$$\eqalign{
& {\text{We have the rectangular coordinates }}\left( {x,y} \right) = \left( {0, - 5} \right) \cr
& {\text{The polar coordinates are:}} \cr
& r = \sqrt {{x^2} + {y^2}} \cr
& r = \sqrt {{{\left( 0 \right)}^2} + {{\left( { - 5} \right)}^2}} \cr
& r = 5 \cr
& \tan \theta = \frac{{ - 5}}{0} \cr
& \theta = {\tan ^{ - 1}}\left( {\frac{{ - 5}}{0}} \right) \cr
& \theta = \frac{{3\pi }}{2},{\text{ }}\theta = \frac{\pi }{2} \cr
& {\text{Therefore}}{\text{, the polar coordinates are:}} \cr
& \left( {r,\theta } \right) = \left( {5,\frac{{3\pi }}{2}} \right),\left( { - 5,\frac{\pi }{2}} \right) \cr} $$