Answer
$\frac{8}{3}$.
Work Step by Step
We can see that the ratio of subsequent terms is $\frac{1}{4}$, thus $r=\frac{1}{4}$.
The sum of the first $n$ terms can be obtained by multiplying the first term($a_1$) by the difference of $1$ and the common ratio ($r$) on the power of $n$ divided by the difference of $1$ and the common ratio ($r$). So $S_n=\frac{a_1(1-r^n)}{1-r}$.
Hence here $S_{5}=\frac{2(1-(\frac{1}{4})^{5})}{1-\frac{1}{4}}=\frac{8}{3}$.
