Answer
$\frac{15}{2}$
Work Step by Step
An infinite geometric series has a sum if and only if $|r|\lt1$, where $r$ is the common ratio. If it exists, then it equals $\frac{a_1}{1-r}$ where $a_1$ is the first term.
Here $r=\frac{1}{3},a_1=5$
$|\frac{1}{3}|\lt1$, thus the sum exists.
Hence the sum: $\dfrac{5}{1-\frac{1}{3}}=\frac{15}{2}$
