We have carried out 870 \mu m observations in the J1040.7-1155 field , known to host an overdensity of Lyman break galaxies at z = 5.16 \pm 0.05 .
We do not detect any individual source at the S _ { 870 \mu \mathrm { m } } = 3.0 mJy / beam ( 2 \sigma ) level .
A stack of nine spectroscopically confirmed z > 5 galaxies also yields a non-detection , constraining the submillimeter flux from a typical galaxy at this redshift to S _ { 870 \mu \mathrm { m } } < 0.85 mJy , which corresponds to a mass limit M _ { \mathrm { dust } } < 1.2 \times 10 ^ { 8 } M _ { \odot } ( 2 \sigma ) .
This limits the mass of thermal dust in distant Lyman break galaxies to less than one tenth of their typical stellar mass .
We see no evidence for strong submillimeter galaxies associated with the ultraviolet-selected galaxy overdensity , but can not rule out the presence of fainter , less massive sources .