How do I find the sum of the infinite geometric series such that a_1=-5 and r=1/6?

For the infinite geometric series $S = {a}_{1} + {a}_{1} r + {a}_{1} {r}^{2} + \cdots$ we can use the formula $S = {a}_{1} / \left(1 - r\right)$ as long as $| r | < 1$.
In our case, ${a}_{1} = - 5 , r = \frac{1}{6}$ and $| r | = | \frac{1}{6} | = \frac{1}{6} < 1$ so
$S = \frac{- 5}{1 - \frac{1}{6}} = \frac{- 5}{\frac{5}{6}} = - 5 \cdot \frac{6}{5} = - 6$