Answer
$\dfrac{5}{2} -i \dfrac{5 \sqrt 3}{2}$
Work Step by Step
The given complex number can be written in the rectangular form as follows: $r (\cos \theta +i \sin \theta) = a+i b$
Where, $a=r \cos \theta ; b =r \sin \theta $
Let us suppose that $z =5(\cos 300^{\circ} +i \sin 300^{\circ} ) ....(1) $
Now, $\cos 300^{\circ}=\cos (360^{\circ} -60^{\circ}) =\cos 60^{\circ}=\dfrac{1}{2}$ and $\sin 300^{\circ}=\sin (360^{\circ} -60^{\circ}) =-\sin 60^{\circ}=\dfrac{-\sqrt 3}{2}$
Therefore, the equation (1) becomes:
$z= 5(\dfrac{1}{2} +i \dfrac{-\sqrt 3}{2})=\dfrac{5}{2} -i \dfrac{5 \sqrt 3}{2}$
