Answer
See below
Work Step by Step
Given $$ A=\begin{bmatrix}
1 & 2 & 0 & 0 & 0\\
3 & 4 & 0 & 0 & 0\\
0 & 0 & 5 & 0 & 0\\
0 & 0 & 0 & 6 & 7\\
0 & 0 & 0 & 8 & 9
\end{bmatrix}$$
So, we get
$det (A)=\begin{vmatrix}
1 & 2 & 0 & 0 & 0\\
3 & 4 & 0 & 0 & 0\\
0 & 0 & 5 & 0 & 0\\
0 & 0 & 0 & 6 & 7\\
0 & 0 & 0 & 8 & 9
\end{vmatrix}\\
=\begin{vmatrix}
1 & 2 & 0 \\ 3 & 4 & 0 \\ 0 & 0 & 5
\end{vmatrix}.\begin{vmatrix}
6 & 7 \\ 8 & 9
\end{vmatrix}\\
=5.(1.4-2.3).(6.9-7.8)\\
=5.(4-6)(54-56)\\
=5.(-2).(-2)\\
=20$
