Answer
$$23 \sqrt{3}$$
Work Step by Step
Since
\begin{align*}
M&=\int_{-\sqrt{3} / 2}^{\sqrt{3} / 2} \int_{4 y^{2}}^{\sqrt{12-4 y^{2}}} 5 x d x d y\\
&=5 \int_{-\sqrt{3} / 2}^{\sqrt{3} / 2}\left[\frac{x^{2}}{2}\right]_{4 y^{2}}^{\sqrt{12-4 y^{2}}} d y\\
&=\frac{5}{2} \int_{-\sqrt{3} / 2}^{\sqrt{3} / 2}\left(12-4 y^{2}-16 y^{4}\right) d y\\
&= \frac{5}{2}\left(12y-\frac{4}{3} y^{3}-\frac{16}{5} y^{5}\right) \bigg|_{-\sqrt{3} / 2}^{\sqrt{3} / 2} \\
&=23 \sqrt{3}
\end{align*}
