Factor $12=2^{2}\times 3$. Rewrite the square root of the product $\sqrt{2^{2}\times 3}$ as the product of square roots $\sqrt{2^{2}}\sqrt{3}$. Take the square root of $2^{2}$.
$$\frac{5\times 2\sqrt{3}}{\sqrt[6]{27}}$$
Multiply $5$ and $2$ to get $10$.
$$\frac{10\sqrt{3}}{\sqrt[6]{27}}$$
Rewrite $\sqrt[6]{27}$ as $\sqrt[6]{3^{3}}$. Convert from radical to exponential form and cancel out $3$ in the exponent. Convert back to radical form.
