We present detections at 850 μm of the Lyman-break galaxy (LBG) population at z 3, 4, and 5 using data from the Submillimetre Common User Bolometer Array 2 Cosmology Legacy Survey in the United Kingdom Infrared Deep Sky Survey ‘Ultra Deep Survey’ field. We employ stacking to probe beneath the survey limit, measuring the average 850 μm flux density of LBGs at z 3, 4, and 5 with typical ultraviolet luminosities of L 1700 10 29 erg s –1 Hz –1 . We measure 850 μm flux densities of (0.25 ± 0.03), (0.41 ± 0.06), and (0.88 ± 0.23) mJy, respectively, finding that they contribute at most 20 per cent to the cosmic far-infrared (IR) background at 850 μm. Fitting an appropriate range of spectral energy distributions to the z ~ 3, 4, and 5 LBG stacked 24–850 μm fluxes, we derive IR luminosities of L 8-1000 μm 3.2, 5.5, and 11.0 10 11 L [and star formation rates (SFRs) of 50–200 M yr –1 ], respectively. We find that the evolution in the IR luminosity density of LBGs is broadly consistent with model predictions for the expected contribution of luminous-to-ultraluminous IR galaxies at these epochs. We observe a positive correlation between stellar mass and IR luminosity and confirm that, for a fixed mass, the reddest LBGs (UV slope β -〉 0) are redder due to dust extinction, with SFR(IR)/SFR(UV) increasing by about an order of magnitude over –2 〈 β 〈 0 with SFR(IR)/SFR(UV) ~ 20 for the reddest LBGs. Furthermore, the most massive LBGs tend to have higher obscured-to-unobscured ratios, hinting at a variation in the obscuration properties across the mass range.