Answer
Please see the graph.
Work Step by Step
$f(x) = (x-2)^2+5$
Axis of symmetry:
$f(x) = (x-2)^2+5$
$f(x) = (x- 2)^2+5$
$x=2$
Vertex:
$f(x) = (x-2)^2+5$
$f(2) = (2-2)^2+5$
$f(2)=0^2+5$
$f(2) = 0+5$
$f(2)=5$
The green line $x=2$ is the axis of symmetry, the black dot at $(2,5)$ is the vertex, and the red line is the function $f(x)=(x-2)^2+5$.