Answer
$0$
Work Step by Step
By using the cofactor expansion along the first row:
$det\begin{vmatrix}
0&a&0\\
b&c &d\\
0&e &0
\end{vmatrix}$
$=0\times det\begin{vmatrix}
c&d\\
e&0
\end{vmatrix}-a\times det\begin{vmatrix}
b &d\\
0&0
\end{vmatrix}+0\times det\begin{vmatrix}
b&c\\
0&e
\end{vmatrix}$
$=0-a(0-0)+0$
$=0$
