A right triangle $PQR$ has a right angle at $R$. The sides $p$, $q$, and $r$ are opposite the angles $P$, $Q$, and $R$, respectively. Calculate the lengths of sides $p$ and $q$ if $r=5$ and $Q=\frac{\pi }{6}$.

$p=\(\frac{5\sqrt3}{2}\)~\(\text{units}\)$

$q=\(\frac\)52~\(\text{units}\)$

$p=\frac{5}{2}\text{ units}$

$q=\frac{5\sqrt{3}}{2}\text{ units}$

$p=\frac{5\sqrt{2}}{2}\text{ units}$

$q=\frac{5}{2}\text{ units}$

$p=\frac{5}{2}\text{ units}$

$q=\frac{5\sqrt{2}}{2}\text{ units}$