已知$\left\{a_n\right\}$是首项为1的等比数列，$S_n$是$\left\{a_n\right\}$的前n项和，且$9S_3=S_5$，则数列$\left\{\frac{1}{a_n}\right\}$的前5项和为

A．

$\frac{15}{8}$或5

B．

$\frac{31}{16}$或5

C．

$\frac{31}{16}$

D．

$\frac{15}{8}$