We present 1.2 mm MAMBO-2 observations of a field which is overdense in Lyman break galaxies (LBGs) at z ∼ 5. The field includes seven spectroscopically confirmed LBGs contained within a narrow (z = 4.95 ± 0.08) redshift range and an eighth at z = 5.2. We do not detect any individual source to a limit of 1.6 mJy/beam (2 × rms). When stacking the flux from the positions of all eight galaxies, we obtain a limit to the average 1.2 mm flux of these sources of 0.6 mJy/beam. This limit is consistent with far-infrared (FIR) imaging in other fields which are overdense in ultraviolet-bright galaxies at z ∼ 5. Independently and combined, these limits constrain the FIR luminosity (8–1000 μm) to a typical z ∼ 5 LBG of LFIR ≲ 3 × 1011 L⊙, implying a dust mass of Mdust ≲ 108 M⊙ (both assuming a grey body at 30 K). This LFIR limit is an order of magnitude fainter than the LFIR of lower redshift submillimetre sources (z ∼ 1–3). We see no emission from any other sources within the field at the above-mentioned level. While this is not unexpected, given millimetre source counts, the clustered LBGs trace significant overdense large-scale structure in the field at z = 4.95. The lack of any such detection in either this or the previous work implies that massive, obscured star-forming galaxies may not always trace the same structures as overdensities of LBGs, at least on the length scale probed here. We briefly discuss the implications of these results for future observations with ALMA.