Answer
$(-1, 5)$
Work Step by Step
$g(x) =(x+1)^2+5$
For a graph in the form $f(x) = a(x-h)^2+k$, the axis of symmetry is the line $x=h$.
$g(x) =(x+1)^2+5$
$g(x) =(x- -1)^2+5$
Axis of symmetry
$x=-1$
Vertex
$x=-1$
$g(x) =(x+1)^2+5$
$g(-1) =(-1+1)^2+5$
$g(-1)=0^2+5$
$g(-1)=0+5$
$g(-1)=5$