Answer
Quadrant III
Work Step by Step
$\frac{-5\pi}{6}$ radians
It is a negative angle and obtained by rotating the terminal side clockwise $\frac{5\pi}{6}$ = $\pi$ - $\frac{\pi}{6}$ radians.
We use |$\frac{-5\pi}{6}$| or $\frac{5\pi}{6}$ to determine the rotation.
So $\frac{5\pi}{6}$ radians lies in quadrant III.
Find the attachment.