Answer
$-\frac{2\sqrt 3}{3}$
Work Step by Step
Recall that $\cos (\pi-x)=-\cos x$ and $\sec \theta=\frac{1}{\cos \theta}$
$\cos \frac{5\pi}{6}=\cos (\pi-\frac{\pi}{6})=-\cos\frac{\pi}{6}=-\frac{\sqrt 3}{2}$
$\sec \frac{5\pi}{6}=\frac{1}{\cos\frac{5\pi}{6}}=\frac{1}{-\frac{\sqrt 3}{2}}$
$=-\frac{2}{\sqrt 3}\cdot\frac{\sqrt 3}{\sqrt 3}=-\frac{2\sqrt 3}{3}$
