Answer
$ \frac{\sqrt 2+\sqrt 6}{4}$
Work Step by Step
$sin\frac{5\pi}{12}=sin(\frac{\pi}{6}+\frac{\pi}{4})=sin\frac{\pi}{6} cos\frac{\pi}{4}+cos\frac{\pi}{6} sin\frac{\pi}{4}=(\frac{1}{2})(\frac{\sqrt 2}{2})+(\frac{\sqrt 3}{2})(\frac{\sqrt 2}{2})=\frac{\sqrt 2+\sqrt 6}{4}$