Answer
$\frac{1055}{27}$.
Work Step by Step
The sum of a geometric sequence until $n$ can be obtained by the formula $S_n=a_1(\frac{1-r^n}{1-r})$ where $a_1$ is the first term and $r$ is the common ratio.
Here $a_1=15,r=\frac{2}{3},n=5$
Hence here the sum is: $S_n=15(\frac{1-(\frac{2}{3})^5}{1-\frac{2}{3}})=\frac{1055}{27}$.
