We investigate the long-standing question of the effect of proton-antiproton annihilation on the (anti-)proton yield, while respecting detailed balance for the 5-body back-reaction for the first time in a full microscopic description of the late stages of heavy-ion collisions. This is achieved by employing a stochastic collision criterion in a hadronic transport approach (SMASH), which allows to treat arbitrary multi-particle reactions. It is used to account for the regeneration of (anti-)protons via $5pirightarrow pbar{p}$. Our results show that a back-reaction happens for a fraction of 15-20% of all annihilations. Within a viscous hybrid approach Au+Au/Pb+Pb collisions from $sqrt{s_{NN}}=17.3$ GeV$-5.02$ TeV are investigated and the quoted fraction is independent of the beam energy or centrality of the collision. Taking the back-reaction into account results in regeneration of half of the (anti-)proton yield that is lost due to annihilations at midrapidity. We also find that, concerning the multiplicities, treating the back-reaction as a chain of 2-body reactions is equivalent to a single 5-to-2 reaction.
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