Use the infinite geometric series formula(shown below) and set it equal to $10$. Then solve for $x$.

$S_{n}=\frac{a_{1}}{1-x}$

$a_{1} = 5$

$\:\:\:5 = 10\left(1 − x\right)$
$\:\:\:5 = 10 − 10x$
$−5 = −10x$