Answer
$$y\left( t \right) = C{e^{ - 5t}}{\text{ is a solution of the given differential equation}}$$
Work Step by Step
$$\eqalign{
& y\left( t \right) = C{e^{ - 5t}} \cr
& {\text{differentiate}} \cr
& y'\left( t \right) = C\left( { - 5{e^{ - 5t}}} \right) \cr
& y'\left( t \right) = - 5C{e^{ - 5t}} \cr
& {\text{replace }}y\left( t \right){\text{ and }}y'\left( t \right){\text{ in the differential equation }} \cr
& y'\left( t \right) + 5y = 0 \cr
& - 5C{e^{ - 5t}} + 5\left( {C{e^{ - 5t}}} \right) \cr
& {\text{simplify}} \cr
& 0 = 0 \cr
& {\text{then}} \cr
& y\left( t \right) = C{e^{ - 5t}}{\text{ is a solution of the given differential equation}} \cr} $$
