  The study of scattering encounters continues to provide new insights into the
general relativistic two-body problem. The local-in-time conservative dynamics
of an aligned-spin binary, for both unbound and bound orbits, is fully encoded
in the gauge-invariant scattering-angle function, which is most naturally
expressed in a post-Minkowskian (PM) expansion, and which exhibits a remarkably
simple dependence on the masses of the two bodies (in terms of appropriate
geometric variables). This dependence links the PM and small-mass-ratio
approximations, allowing gravitational self-force results to determine new
post-Newtonian (PN) information to all orders in the mass ratio. In this paper,
we exploit this interplay between relativistic scattering and self-force theory
to obtain the third-subleading (4.5PN) spin-orbit dynamics for generic spins,
and the third-subleading (5PN) spin$_1$-spin$_2$ dynamics for aligned spins. We
further implement these novel PN results in an effective-one-body framework,
and demonstrate the improvement in accuracy by comparing against
numerical-relativity simulations.
