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 similar to 5. We use the luminosity and velocity width (full width at half-maximum, FWHM, of similar or equal to 160 km s(-1)) of the CO(2-1) line emission to constrain the gas and dynamical mass of M-gas similar or equal to 1.6 x 10(10) M-circle dot and M-dyn(< 2 kpc) similar or equal to 5 x 10(10) (0.25/sin(2)i) M-circle dot, respectively, similar to that observed for SMGs at lower redshifts of z similar to 2-4, although we note that our observed CO FWHM is a factor of similar to 3 narrower than typically seen in SMGs. Together with the stellar mass we estimate a total baryonic mass of M-bary similar or equal to 1 x 10(11) M-circle dot, 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 similar to 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 similar to 4-5 SMGs possess the baryonic masses and gas consumption time-scales necessary to be the progenitors of the luminous old red galaxies seen at z similar to 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.