Answer
$$ \dfrac{ \sqrt 3}{2}$$
Work Step by Step
Apply the sum formula:
$\sin(A+B)=\sin(A)\cos(B)+\cos(A)\sin(B)$
Therefore,
$$\sin (\dfrac{\pi}{18}) \ \cos(\dfrac{5 \pi}{18}) +\cos (\dfrac{ \pi}{18}) \ \sin(\dfrac{5 \pi}{18})\\
=\sin \ (\dfrac{\pi}{18} +\dfrac{5 \pi}{18})\\
=\sin \ (\dfrac{ \pi}{3})\\
= \dfrac{ \sqrt 3}{2}$$
