An infinite GP has first term x and sum 5, then 

We know that, the sum of infinite terms of GP is

$\begin{array}{l}{\mathrm{S}}_{\mathrm{\infty }}=\left\{\begin{array}{ll}\frac{a}{1-r},& \left|r\right|<1\\ ,\mathrm{\infty }& \left|r\right|\ge 1\end{array}\right.\\ \therefore {\mathrm{S}}_{\mathrm{\infty }}=\frac{x}{1-r}=5(\because |r|<1)\end{array}$

or $1-r=\frac{x}{5}$

$\text{ i.e., }-1<\frac{5-x}{5}<1$

or, $-10<-x<0$

or, $0<x<10$