Step 1 :The equation \(f(x)=(x-8)^{2}+5\) is a transformation of the equation \(y=x^{2}\).
Step 2 :The transformation involves a shift to the right by 8 units and a shift upwards by 5 units.
Step 3 :This is because the term \((x-8)\) in the equation shifts the graph to the right by 8 units and the term \(+5\) shifts the graph upwards by 5 units.
Step 4 :\(\boxed{\text{C. a translation 8 units to the right and 5 units up}}\)