Answer
$$3$$
Work Step by Step
\begin{align*}
M&=\int_{-1}^{1} \int_{z-1}^{1-z} \int_{0}^{\sqrt{z}}(2 y+5) d y d x d z\\
&=\int_{0}^{1} \int_{z-1}^{1-z}(z+5 \sqrt{z}) d x d z\\
&=\int_{0}^{1} 2(z+5 \sqrt{z})(1-z) d z\\
&=2 \int_{0}^{1}\left(5 z^{1 / 2}+z-5 z^{3 / 2}-z^{2}\right) d z\\
&=2\left[\frac{10}{3} z^{3 / 2}+\frac{1}{2} z^{2}-2 z^{5 / 2}-\frac{1}{3} z^{3}\right]_{0}^{1}\\
&=2\left(\frac{9}{3}-\frac{3}{2}\right)=3
\end{align*}
