  Quantum theory permits interference between indistinguishable paths but, at
the same time, restricts its order. Single-particle interference, for instance,
is limited to the second order, that is, to pairs of single-particle paths. To
date, all experimental efforts to search for higher-order interferences beyond
those compatible with quantum mechanics have been based on such single-particle
schemes. However, quantum physics is not bounded to single-particle
interference. We here experimentally study many-particle higher-order
interference using a two-photon-five-slit setup. We observe nonzero
two-particle interference up to fourth order, corresponding to the interference
of two distinct two-particle paths. We further show that fifth-order
interference is restricted to $10^{-3}$ in the intensity-correlation regime and
to $10^{-2}$ in the photon-correlation regime, thus providing novel bounds on
higher-order quantum interference.
