From the V-shape of the graph, we see that the base function is an absolute value function, or
y=|x|.
The slope of each arm is ± (10-5)/5 = 2, so
the function with the vertex at origin is y=2|x|.
To move the vertex to the RIGHT by 5 units, we replace x by x-5, or
y=2|x-5|
We are given this function equals h(x)-5, or
h(x)-5 = 2|x-5|
solving for h(x) gives
h(x)=2|x-5|+5 (red curve)
We are also told that h(x) is a reflection about the y-axis, i.e.
f(x)=h(-x)
=2|-x-5|+5
=2|x+5|+5 because |X+A|=|-X-A|
which is the green line shown in the attached graph.