  The present work considers systems whose dynamics are governed by the
nonlinear interactions among groups of 6 nonlinear waves, such as those
described by the unforced quintic nonlinear Schr\"odinger equation. Specific
parameter regimes in which ensemble-averaged dynamics of such systems with
finite size are accurately described by a wave kinetic equation, as used in
wave turbulence theory, are theoretically predicted. In addition, the
underlying reasons that the wave kinetic equation may be a poor predictor of
wave dynamics outside these regimes are also discussed. These theoretical
predictions are directly verified by comparing ensemble averages of solutions
to the dynamical equation with corresponding solutions of the wave kinetic
equation.
