Résumé : Inclusive jet cross sections are measured in photoproduction at HERA using the HI detector. The data sample of e+p → e+ + jet + X events in the kinematic range of photon virtualities Q2 ≤ 1GeV2 and photon-proton centre-of-mass energies 95 ≤ W γp ≤ 285GeV represents an integrated luminosity of 24.1pb-1. Jets are defined using the inclusive k⊥ algorithm. Single- and multi-differential cross sections are measured as functions of jet transverse energy ETjet and pseudorapidity η jet in the domain 5 ≤ ETjet ≤ 75GeV and -1 ≤ ηjet ≤ 2.5. The cross sections are found to be in good agreement with next-to-leading order perturbative QCD calculations corrected for fragmentation and underlying event effects. The cross section differential in ETjet, which varies by six orders of magnitude over the measured range, is compared with similar distributions from pp̄ colliders at equal and higher energies.