Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 71

$-\dfrac{5i}{6}$

Multiplying the denominator by $i$, the given expression, $ \dfrac{5}{6i} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{5}{6i}\cdot\dfrac{i}{i} \\\\= \dfrac{5i}{6i^2} \\\\= \dfrac{5i}{6(-1)} \\\\= \dfrac{5i}{-6} \\\\= -\dfrac{5i}{6} .\end{array}