  The centrality dependence of the $p/\pi$ ratio measured by the ALICE
Collaboration in 5.02 TeV Pb-Pb collisions indicates a statistically
significant suppression with the increase of the charged particle multiplicity
once the centrality-correlated part of the systematic uncertainty is eliminated
from the data. We argue that this behavior can be attributed to baryon
annihilation in the hadronic phase. By implementing the $B\bar{B}
\leftrightarrow 5\pi$ reaction within a generalized partial chemical
equilibrium framework, we estimate the annihilation freeze-out temperature at
different centralities, which decreases with increasing charged multiplicity
and yields $T_{\rm ann} = 132 \pm 5$ MeV in 0-5% most central collisions. This
value is considerably below the hadronization temperature of $T_{\rm had} \sim
160$ MeV but above the thermal (kinetic) freeze-out temperature of $T_{\rm kin}
\sim 100$ MeV. Baryon annihilation reactions thus remain relevant in the
initial stage of the hadronic phase but freeze out before (pseudo-)elastic
hadronic scatterings. One experimentally testable consequence of this picture
is a suppression of various light nuclei to proton ratios in central collisions
of heavy ions.
