\(\displaystyle f'(x) = \frac{x^{2}}{2} - 2x + C \)

\(\displaystyle f(x) = \frac{x^{3}}{6} - x^{2} + Cx + D \)

\(\displaystyle f(1) = 0 = \frac{1}{6} -1 + C + D \)

\(\displaystyle f(5) = 0 = \frac{125}{6} - 25 + 5C + D \)

now just solve the above two equations simultaneously to find the values of C and D