Explanation

(c)
As we know, sum infinite terms of GP,
$S_{\infty} = \left\{ \begin{array}{r}
\frac{a}{1 - r}, \\
\infty,
\end{array} \right.\ \ \begin{matrix}
|r| < 1 \\
|r| \geq 1
\end{matrix}$
$\therefore\ \ S_{\infty} = \frac{x}{1 - r} = 5$ $\{ thus\ |r| < 1\}$
$\Rightarrow 1 - r = \frac{x}{5}$
$\Rightarrow r = \frac{5 - x}{5}$ exists only when $|r| < 1$
$\Rightarrow - 1 < \frac{5 - x}{5} < 1$
$\therefore\ - 10 < - x < 0\ \Rightarrow 0 < x < 10$