The electrophoretic mobility of large spherical colloids in different salt solutions of varying valency and concentration is studied via a combination approach of numerically solving the standard electrokinetic model with a zeta potential that has been obtained from explicit ion simulations of the restricted primitive model, thus going beyond the standard mean-field treatment. We compare our theoretical mobility curves to two distinct sets of experimental results and obtain good agreement for monovalent and divalent salt solutions. For the case of the trivalent La3+ salt, the experimentally obtained mobility reversal at high ionic strengths can be obtained only by adding an additional attractive interaction of 4k(B)T to the potential between the colloid and La3+, hinting at the presence of a nonelectrostatic binding term for this ion. It is also shown that, contrary to intuition, charge inversion does not necessarily result in mobility reversal.