Via a Laplace expansion across the first column, you have
[tex]\begin{vmatrix}-4&-4&-3\\3&3&-5\\-5&2&5\end{vmatrix}=-4\begin{vmatrix}3&-5\\2&5\end{vmatrix}-3\begin{vmatrix}-4&-3\\2&5\end{vmatrix}-5\begin{vmatrix}-4&-3\\3&-5\end{vmatrix}[/tex]
[tex]=-4(15-(-10))-3(-20-(-6))-5(20-(-9))[/tex]
[tex]=-203[/tex]
