  The thermal Hall conductance $K$ of the fractional quantum Hall state at
filling fraction $\nu=5/2$ has recently been measured to be $K=2.5
\pi^2k_B^2T/3h$ [M. Banerjee et al., Nature ${\bf 559}$, 205 (2018)]. The
half-integer value of this result (in units of $\pi^2k_B^2T/3h$) provides
strong evidence for the presence of a Majorana edge mode and a corresponding
quantum Hall state hosting quasiparticles with non-Abelian statistics. Whether
this measurement points to the realization of the PH-Pfaffian or the
anti-Pfaffian state has been the subject of debate. Here we consider the
implications of this measurement for anti-Pfaffian edge-state transport. We
show that in the limit of a strong Coulomb interaction and an approximate spin
degeneracy in the lowest Landau level, the anti-Pfaffian state admits
low-temperature edge phases that are consistent with the Hall conductance
measurements. These edge phases can exhibit fully-equilibrated electrical
transport coexisting with partially-equilibrated heat transport over a range of
temperatures. Through a study of the kinetic equations describing
low-temperature electrical and heat transport of these edge states, we
determine regimes of parameter space, controlling the interactions between the
different edge modes, that agree with experiment.
