Answer
$${S_5} = 1705$$
Work Step by Step
$$\eqalign{
& {a_1} = 5,{a_2} = 20,{a_3} = 80,{a_4} = 320,... \cr
& {\text{to verify that the sequence is geometric}}{\text{, divide each term except the first by }} \cr
& {\text{the preceding term}} \cr
& \frac{{{a_4}}}{{{a_3}}} = \frac{{320}}{{80}} = 4 \cr
& \frac{{{a_3}}}{{{a_2}}} = \frac{{80}}{{20}} = 4 \cr
& \frac{{{a_2}}}{{{a_1}}} = \frac{{20}}{5} = 4 \cr
& {\text{the ratio is constant}}{\text{, so the sequence is geometric with }}r = 4 \cr
& {\text{then the sum of the first }}n{\text{ terms}}{\text{ is given by}} \cr
& {S_n} = \frac{{{a_1}\left( {{r^n} - 1} \right)}}{{r - 1}},{\text{ where }}r \ne 1 \cr
& {\text{let }}n = 5,\,\,\,{a_1} = 5{\text{ and }}r = 4 \cr
& {S_5} = \frac{{\left( 5 \right)\left( {{4^5} - 1} \right)}}{{4 - 1}} \cr
& {S_5} = \frac{{\left( 5 \right)\left( {1023} \right)}}{3} \cr
& {\text{simplifying}} \cr
& {S_5} = 1705 \cr} $$
