  This second article in a two-part series (following [arXiv:2105.02865],
listed here as \cite{L}) proves optimal pointwise decay rates for the quintic
defocusing wave equation with large initial data on nonstationary spacetimes,
and both the quintic defocusing and quintic focusing wave equations with small
initial data on nonstationary spacetimes. We prove a weighted local energy
decay estimate, and use local energy decay and Strichartz estimates on these
variable-coefficient backgrounds. By using an iteration scheme, we obtain the
optimal pointwise bounds. In addition, we explain how the iteration scheme
reaches analogous pointwise bounds for other integral power nonlinearities that
are either higher or lower than the quintic power, given the assumption of
global existence for those powers (and in the case of the lower powers, given
certain initial decay rates).
