Answer
$${S_5} = - 1705$$
Work Step by Step
$$\eqalign{
& {\text{the sum of the first }}n{\text{ terms of a geometric sequence}}{\text{ is given by}} \cr
& {S_n} = \frac{{{a_1}\left( {{r^n} - 1} \right)}}{{r - 1}},{\text{ where }}r \ne 1 \cr
& {\text{let }}n = 5,\,\,\,{a_1} = - 5{\text{ and }}r = 4 \cr
& {S_5} = \frac{{\left( { - 5} \right)\left( {{{\left( 4 \right)}^5} - 1} \right)}}{{4 - 1}} \cr
& {\text{simplifying}} \cr
& {S_5} = \frac{{\left( { - 5} \right)\left( {1023} \right)}}{3} \cr
& {S_5} = - 1705 \cr} $$
