We address the effect of quintic nonlinearities in the propagation of optical solitons in cubic nonlinear media. Our focus is on the decay of higher-order solitons in the presence of self-defocusing quintic perturbations. We show that, in spite of the fact that the governing evolution equations are symmetric, the quintic nonlinearity produces the asymmetrical self-splitting of the solitons. We study in detail the self-splitting process and compare the results with the soliton evolution with self-focusing quintic perturbations.