Answer
$$y = 2{\sin ^{ - 1}}\left( {\frac{x}{5}} \right)$$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dx}} = \frac{2}{{\sqrt {25 - {x^2}} }} \cr
& {\text{Separate the variables}} \cr
& dy = \frac{2}{{\sqrt {25 - {x^2}} }}dx \cr
& {\text{Integrate both sides}} \cr
& \int {dy} = \int {\frac{2}{{\sqrt {25 - {x^2}} }}} dx \cr
& y = 2{\sin ^{ - 1}}\left( {\frac{x}{5}} \right) + C{\text{ }}\left( {\bf{1}} \right) \cr
& {\text{Use the initial condition }}\left( {5,\pi } \right) \cr
& \pi = 2{\sin ^{ - 1}}\left( {\frac{5}{5}} \right) + C \cr
& \pi = 2\left( {\frac{\pi }{2}} \right) + C \cr
& C = 0 \cr
& {\text{Substitute }}C{\text{ into }}\left( {\bf{1}} \right) \cr
& y = 2{\sin ^{ - 1}}\left( {\frac{x}{5}} \right) \cr
& \cr
& {\text{Graph}} \cr} $$
