#### Answer

$${S_5} \approx 464.4$$

#### Work Step by Step

$$\eqalign{
& {\text{the sum of the first }}n{\text{ terms of a geometric sequence}}{\text{ is given by}} \cr
& {S_n} = \frac{{{a_1}\left( {{r^n} - 1} \right)}}{{r - 1}},{\text{ where }}r \ne 1 \cr
& {\text{let }}n = 5,\,\,\,{a_1} = 6.324{\text{ and }}r = 2.598 \cr
& {S_5} = \frac{{\left( {6.324} \right)\left( {{{\left( {2.598} \right)}^5} - 1} \right)}}{{2.598 - 1}} \cr
& {\text{simplifying}} \cr
& {S_5} \approx 464.4 \cr} $$