  The nonlinear response of stochastic models obeying a master equation is
calculated up to fifth-order in the external field thus extending the
third-order results obtained earlier (G. Diezemann, Phys. Rev. E{\bf 85},
051502 (2012)). For sinusoidal fields the $5\om$-component of the
susceptibility is computed for the model of dipole reorientations in an
asymmetric double well potential and for a trap model with a Gaussian density
of states. For most realizations of the models a hump is found in the
higher-order susceptibilities. In particular, for the asymmetric double well
potential model there are two characteristic temperature regimes showing the
occurence of such a hump as compared to a single characteristic regime in case
of the third-order response. In case of the trap model the results strongly
depend on the variable coupled to the field. As for the third-order response,
the low-frequency limit of the susceptibility plays a crucial role with respect
to the occurence of a hump. The findings are discussed in light of recent
experimental results obtained for supercooled liquids. The differences found
for the third-order and the fifth-order response indicate that nonlinear
response functions might serve as a powerful tool to discriminate among the
large number of existing models for glassy relaxation.
