The axis (of symmetry) of a parabola is the line passing through the vertex. In "your" parabola, it is the vertical line passing through the highest point of the arch.
The maximum height of your parabola
h(x) = -(5/64)x^2 +4
is, by using x = -b /2a,
x = -0 / 2(-5/64) = 0 ----------this means the axis of symmetry is at x=0, which is the y-axis in your graph.
h(0) = 0 +4 = 4
That only means that the maximum height of your parabola is 4 ft only.
In your graph, the vertex, or maximum height is at point (0,4).