We have detected the CO ( 2–1 ) transition from the submillimetre galaxy ( SMG ) LESS J033229.4 - 275619 at z = 4.755 using the new Compact Array Broadband Backend system on the Australian Telescope Compact Array . These data have identified a massive gas reservoir available for star formation for the first time in an SMG at z \sim 5 . We use the luminosity and velocity width ( FWHM of \simeq 160 km s ^ { -1 } ) of the CO ( 2–1 ) line emission to constrain the gas and dynamical mass of M _ { \mathrm { gas } } \simeq 1.6 \times 10 ^ { 10 } M _ { \odot } and M _ { \mathrm { dyn } } ( < 2 \mathrm { kpc } ) \simeq 5 \times 10 ^ { 10 } ( 0.25/sin ^ { 2 } i ) M _ { \odot } , respectively , similar to that observed for SMGs at lower redshifts of z \sim 2 –4 , although we note that our observed CO FWHM is a factor of \sim 3 narrower than typically seen in SMGs . Together with the stellar mass we estimate a total baryonic mass of M _ { \mathrm { bary } } \simeq 1 \times 10 ^ { 11 } M _ { \odot } , consistent with the dynamical mass for this young galaxy within the uncertainties . Dynamical and baryonic mass limits of high-redshift galaxies are useful tests of galaxy formation models : using the known z \sim 4 –5 SMGs as examples of massive baryonic systems , we find that their space density is consistent with that predicted by current galaxy formation models . In addition , these observations have helped to confirm that z \sim 4 –5 SMGs possess the baryonic masses and gas consumption timescales necessary to be the progenitors of the luminous old red galaxies seen at z \sim 3 . Our results provide a preview of the science that ALMA will enable on the formation and evolution of the earliest massive galaxies in the Universe .