This function is continuous everywhere and is differentiable everywhere except x=5.
For x<=5, f(x)=x, f'(x)=1 and for x>-5 f(x)=10-x, f'(x)=-1. So there are no points for which f'(x)=0, and x=5 is the only critical point.
The function f is increasing on `(-oo, 5)` and is decreasing on `(5, +oo)` . So x=5 is a relative maximum.