The cross section for high-E-T dijet production in photoproduction has been measured with the ZEUS detector at HERA using an integrated luminosity of 81.8 pb(-1). The events were required to have a virtuality of the incoming photon, Q(2), of less than 1 GeV2 and a photon-proton center-of-mass energy in the range 142 < W-gamma p < 293 GeV. Events were selected if at least two jets satisfied the transverse-energy requirements of E-T(jet1)> 20 GeV and E-T(jet2)> 15 GeV and pseudorapidity (with respect to the proton beam direction) requirements of -1 <eta(jet1,2)< 3, with at least one of the jets satisfying -1 <eta(jet)< 2.5. The measurements show sensitivity to the parton distributions in the photon and proton and to effects beyond next-to-leading order in QCD. Hence these data can be used to constrain further the parton densities in the proton and photon.