$O=-4x-2x^2+5-2y^2+4y-2xy$
$O=(-x^2-4x-4)+(-y^2+4y-4)+(-x^2-2xy-y^2)+13$
$O=-(x^2+4x+4)-(y^2-4y+4)-(x^2+2xy+y^2)+13$
$O=-(x+2)^2-(y-2)^2-(x+y)^2+13$
Vì $-(x+2)^2-(y-2)^2-(x+y)^2 \le 0 \; \forall x\in \mathbb{R}$
$\Rightarrow -(x+2)^2-(y-2)^2-(x+y)^2+13\le 13$
Vậy $\max O = 13$ khi $\begin{cases}x+2=0\\y-2=0\end{cases} \Leftrightarrow \begin{cases}x=-2\\y=2\end{cases}$