Answer
$${\text{ }}{a_5} = \frac{4}{{25}}$$
Work Step by Step
$$\eqalign{
& {a_3} = 4,\,\,\,r = \frac{1}{5} \cr
& {a_n} = {a_1}{r^{n - 1}} \cr
& {\text{For }}n = 3 \cr
& {a_3} = {a_1}{r^{3 - 1}} \cr
& {a_3} = {a_1}{r^2} \cr
& {\text{Then}} \cr
& 4 = {a_1}{\left( {\frac{1}{5}} \right)^2} \cr
& {\text{Solving for }}{a_1} \cr
& 4 = {a_1}\left( {\frac{1}{{25}}} \right) \cr
& {a_1} = 100 \cr
& {\text{Then }}{a_n} = {a_1}{r^{n - 1}} \cr
& {\text{ }}{a_n} = 100{\left( {\frac{1}{5}} \right)^{n - 1}} \cr
& {\text{Find }}{a_5} \cr
& {\text{ }}{a_5} = 100{\left( {\frac{1}{5}} \right)^{5 - 1}} \cr
& {\text{ }}{a_5} = 100\left( {\frac{1}{{625}}} \right) \cr
& {\text{ }}{a_5} = \frac{4}{{25}} \cr} $$
