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