Answer
$$\left( {0, - \frac{{5\pi }}{6}, - 5} \right)$$
Work Step by Step
$$\eqalign{
& \left( {5, - \frac{{5\pi }}{6},\pi } \right) \cr
& {\text{spherical}}\left( {\rho ,\theta ,\phi } \right):\left( {5, - \frac{{5\pi }}{6},\pi } \right) \to \rho = 5,{\text{ }}\theta = - \frac{{5\pi }}{6},{\text{ }}\phi = \pi \cr
& {\text{Spherical to cylindrical }}\left( {r,\theta ,z} \right),{\text{ }}\left( {r \geqslant 0} \right){\text{ See page 807}} \cr
& {r^2} = {\rho ^2}{\sin ^2}\phi ,{\text{ }}\theta = \theta ,{\text{ }}z = \rho \cos \phi \cr
& {r^2} = {\left( 5 \right)^2}{\sin ^2}\left( \pi \right) = 0 \to r = 0 \cr
& \theta = - \frac{{5\pi }}{6} \cr
& z = 5cos\left( \pi \right) = - 5 \cr
& {\text{The cylindrical }}\left( {r,\theta ,z} \right){\text{ coordinates are:}} \cr
& \left( {0, - \frac{{5\pi }}{6}, - 5} \right) \cr} $$
