We have exploited the large area coverage of the combined UKIDSS Ultra Deep Survey (UDS) and Subaru/XMM–Newton Deep Survey (SXDS) to search for bright Lyman-break galaxies (LBGs) at z≥ 5. Using the available optical + near-infrared photometry to efficiently exclude low-redshift contaminants, we identify nine z≥ 5 LBG candidates brighter than z′AB= 25 within the 0.6-deg2 overlap region between the UDS early data release and the optical coverage of the SXDS. Accounting for selection incompleteness, we estimate the corresponding surface density of z≥ 5 LBGs with z′AB≤ 25 to be 0.005 ± 0.002 arcmin−2. Modelling of the optical + near-infrared photometry constrains the candidates' redshifts to lie in the range 5.1 < z < 5.9, and provides estimates for their stellar masses. Although the stellar mass estimates are individually uncertain, a stacking analysis suggests that the typical stellar mass of the LBG candidates is ≳5 × 1010 M⊙ which, if confirmed, places them amongst the most massive galaxies currently known at z≥ 5. It is found that Lambda cold dark matter structure formation can produce sufficient numbers of dark matter haloes at z≥ 5 to accommodate our estimated number density of massive LBGs for plausible values of σ8 and the ratio of stellar to dark matter. Moreover, it is found that recent galaxy formation models can also account for the existence of such massive galaxies at z≥ 5. Finally, no evidence is found for the existence of LBGs with stellar masses in excess of ≃3 × 1011 M⊙ at this epoch, despite the large comoving volume surveyed.