  In the spirit of effective field theory, the Standard-Model Extension (SME)
provides a comprehensive framework to systematically probe the possibility of
Lorentz/CPT violation. In the pure gravity sector, operators with mass
dimension larger than 4, while in general being advantageous to short-range
experiments, are hard to investigate with systems of astronomical size.
However, there is exception if the leading-order effects are CPT-violating and
velocity-dependent. Here we study the lowest-order operators in the pure
gravity sector that violate the CPT symmetry with carefully chosen relativistic
binary pulsar systems. Applying the existing analytical results to the dynamics
of a binary orbit, we put constraints on various coefficients for Lorentz/CPT
violation with mass dimension 5. These constraints, being derived from the
post-Newtonian dynamics for the first time, are complementary to those obtained
from the kinematics in the propagation of gravitational waves.
