Answer
Please see the graph.
Work Step by Step
$G(x)=-2(x+1)^2+5$
$G(x)=-2(x+1)^2+5$
$G(x)=-2(x+1)(x+1)+5$
$G(x)=-2(x^2+x+x+1)+5$
$G(x)=-2(x^2+2x+1)+5$
$G(x)=-2x^2-4x-2+5$
$G(x)=-2x^2-4x+3$
$a=-2$, $b=-4$, $c=3$
The vertex is at $x=-b/2a$, on the line of symmetry.
$x=-b/2a$
$x=-(-4)/2*-2$
$x=4/-4$
$x=-1$
$G(x)=-2(x+1)^2+5$
$G(-1)=-2(-1+1)^2+5$
$G(-1)=-2(0)^2+5$
$G(-1)=-2*0+5$
$G(-1)=0+5$
$G(-1)=5$
$(-1, 5)$ is the vertex.