Answer
$\dfrac{2\pi}{7}$
Work Step by Step
RECALL:
The following are the means on how to find the reference angle of an angle $\theta$ based on its position:
(1) Quadrant I: $\theta$ (itself)
(2) Quadrant II: $\pi-\theta$
(3) Quadrant III: $\theta - \pi$
(4) Quadrant IV: $2\pi-\theta$
$\dfrac{5\pi}{7}$ is in Quadrant II.
Thus, using formula (2) above gives:
reference angle of $\dfrac{5\pi}{7}$ is $\pi - \dfrac{5\pi}{7}=\dfrac{7\pi}{7}-\dfrac{5\pi}{7} = \dfrac{2\pi}{7}$
