  The variations in Ly$\alpha$ forest opacity observed at $z>5.3$ between lines
of sight to different background quasars are too strong to be caused by
fluctuations in the density field alone. The leading hypothesis for the cause
of this excess variance is a late, ongoing reionization process at redshifts
below six. Another model proposes strong ionizing background fluctuations
coupled to a short, spatially varying mean free path of ionizing photons,
without explicitly invoking incomplete reionization. With recent observations
suggesting a short mean free path at $z\sim6$, and a dramatic improvement in
$z>5$ Ly$\alpha$ forest data quality, we revisit this latter possibility. Here
we apply the likelihood-free inference technique of approximate Bayesian
computation to jointly constrain the hydrogen photoionization rate $\Gamma_{\rm
HI}$ and the mean free path of ionizing photons $\lambda_{\rm mfp}$ from the
effective optical depth distributions at $z=5.0$-$6.1$ from XQR-30. We find
that the observations are well-described by fluctuating mean free path models
with average mean free paths that are consistent with the steep trend implied
by independent measurements at $z\sim5$-$6$, with a concomitant rapid evolution
of the photoionization rate.
