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Evaluate: $\frac{5 \cos^2 60^\circ + 4 \sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \sin^2 60^\circ}$
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$$\begin{aligned}& 5(\frac{1}{2})^2+4(\frac{2}{\sqrt{3}})^2-(1)^2 \\ & (\frac{1}{2})^2+(\frac{\sqrt{3}}{2})^2 \\ & = \frac{67}{12}\end{aligned}$$