Evaluate $\displaystyle : \frac{5 \tan 60^{\circ}}{\left(\sin ^{2} 60^{\circ}+\cos ^{2} 60^{\circ}\right) \tan 30^{\circ}}$

\[\begin{gathered} \frac{5 \tan 60^{\circ}}{\left(\sin ^{2} 60^{\circ}+\cos ^{2} 60^{0}\right) \tan 30^{\circ}} \\ \frac{5 \times \sqrt{3}}{\left[\left(\dfrac{\sqrt{3}}{2}\right)^{2}+\left(\dfrac{1}{2}\right)^{2}\right] \times \dfrac{1}{\sqrt{3}}} \\ =15 \end{gathered} \]