Looking at the series, we have a geometric sequence, where the first term is a1 = 5 and the common ratio is q = -3/5.
(This ratio can be calculated by dividing one term by the term before)
To find the sum of an infinite geometric sequence, we can use the formula below:
[tex]S_{\infty}=\frac{a_1}{1-q}[/tex]Since a1 = 5 and q = -3/5, we have:
[tex]S_{\infty}=\frac{5}{1-(-\frac{3}{5})}=\frac{5}{1+\frac{3}{5}}=\frac{5}{\frac{8}{5}}=5\cdot\frac{5}{8}=\frac{25}{8}[/tex]Therefore the correct option is C.
