Answer
$\dfrac{\sqrt3}{2}$
Work Step by Step
Recall that:
$\sin(\alpha+\beta)=\sin(\alpha)\cos(\beta)+\cos(\alpha)\sin(\beta)$
Hence,
$\sin(\frac{\pi}{18})\cos(\frac{5\pi}{18})+\cos(\frac{\pi}{18})\sin(\frac{5\pi}{18})\\
=\sin\left(\frac{5\pi}{18}+\frac{\pi}{18}\right)\\
=\sin(\frac{\pi}{3})\\
=\frac{\sqrt3}{2}$
