Answer
$\dfrac{341}{128}$
Work Step by Step
Since, we have $S_n=\dfrac{a_1(1-r^{n})}{1-r}$
Here, $n=5,a_1=2,r=\dfrac{1}{4}$
Thus,
$S_{5}=\dfrac{2[1-(\dfrac{1}{4})^{5}]}{1-(\dfrac{1}{4})}=\dfrac{8}{3}(\dfrac{1023}{1024})=\dfrac{341}{128}$