Answer
$15$
Work Step by Step
For efficiency, we begin with a co-factor expansion along the third row, and continue with a co-factor expansion along the first row of the resultant matrix. Note that, in both cases, only one term is non-vanishing.
$
\begin{align}\det A &=
3\begin{vmatrix}0&0&5\\7&2&-5\\3&1&7\end{vmatrix}
=3\cdot5\begin{vmatrix}7&2\\3&1\end{vmatrix}=15(7-6)=15
\end{align}
$
