We report on observations of the dust trail of Comet 67P/Churyumov-Gerasimenko (CG) in visible light with the Wide Field Imager at the ESO/MPG 2.2 m telescope at 4.7 AU before aphelion, and at 24μm with the MIPS instrument on board the Spitzer Space Telescope at 5.7 AU both before and after aphelion. The comet did not appear to be active during our observations. Our images probe large dust grains emitted from the comet that have a radiation pressure parameter β<0.01. We compare our observations with simulated images generated with a dynamical model of the cometary dust environment and constrain the emission speeds, size distribution, production rate and geometric albedo of the dust. We achieve the best fit to our data with a differential size distribution exponent of -4.1, and emission speeds for a β=0.01 particle of 25 m/s at perihelion and 2 m/s at 3 AU. The dust production rate in our model is on the order of 1000 kg/s at perihelion and 1 kg/s at 3 AU, and we require a dust geometric albedo between 0.022 and 0.044. The production rates of large (> 10μm) particles required to reproduce the brightness of the trail are sufficient to also account for the coma brightness observed while the comet was inside 3 AU, and we infer that the cross-section in the coma of CG may be dominated by grains of the order of 60-600μm.