Answer
$$\frac{{dy}}{{d\theta }} = \frac{1}{{\theta \ln 2}}$$
Work Step by Step
$$\eqalign{
& y = {\log _2}5\theta \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}\theta \cr
& \frac{{dy}}{{d\theta }} = \frac{d}{{d\theta }}\left[ {{{\log }_2}5\theta } \right] \cr
& {\text{use the rule }}\frac{d}{{dx}}\left[ {{{\log }_a}u} \right] = \frac{1}{{\ln a}} \cdot \frac{1}{u}\frac{{du}}{{dx}}. \cr
& \frac{{dy}}{{d\theta }} = \frac{1}{{\ln 2}} \cdot \frac{1}{{5\theta }}\frac{d}{{d\theta }}\left[ {5\theta } \right] \cr
& {\text{solve the derivative}} \cr
& \frac{{dy}}{{d\theta }} = \frac{1}{{\ln 2}} \cdot \frac{1}{{5\theta }}\left( 5 \right) \cr
& {\text{simplifying}} \cr
& \frac{{dy}}{{d\theta }} = \frac{1}{{\theta \ln 2}} \cr} $$
