Polar coordinates are written as the distance of the point to the origin and its angle of elevation around the unit cirlce.
Draw a right triangle with an angle of [tex]\frac{\pi}6[/tex] and a hypotenuse with a length of 5.
You can use trigonometric ratios to find the legs of this triangle, which are the x and y coordinates of the point.
[tex]\cos=\frac{adj}{hyp} \\\\ \cos(\frac{\pi}6)=\frac{x}5 \\\\ \frac{\sqrt{3}}2=\frac{x}5 \\\\ \frac{5\sqrt{3}}2=x[/tex]
As for y...
[tex]\sin=\frac{opp}{hyp}\\\\\sin(\frac{\pi}6) = \frac{y}5 \\\\ \frac{1}2=\frac{y}5 \\\\ \frac{5}2=y[/tex]
[tex]\boxed{(\frac{5\sqrt{3}}2,\ \frac{5}2)}[/tex]
