Find the points of local maxima, local minima and the points of inflection of the function f(x) = x5 + 5x4 + 5x3 - 1. Also, find the corresponding local maximum and local minimum values.
f(x) = x5 + 5x4 + 5x3 - 1
or f'(x) = 5x4 - 20 x3 + 15x2
