We have analysed a sample of 1292 4.5 micron-selected galaxies at z>=3, over 0.6 square degrees of the UKIRT Infrared Deep Survey (UKIDSS) Ultra Deep Survey (UDS). Using photometry from the U band through 4.5 microns, we have obtained photometric redshifts and derived stellar masses for our sources. Only two of our galaxies potentially lie at z>5. We have studied the galaxy stellar mass function at 3<=z<5, based on the 1213 galaxies in our catalogue with [4.5]<= 24.0. We find that: i) the number density of M > 10^11 Msun galaxies increased by a factor > 10 between z=5 and 3, indicating that the assembly rate of these galaxies proceeded > 20 times faster at these redshifts than at 0<z<2; ii) the Schechter function slope alpha is significantly steeper than that displayed by the local stellar mass function, which is both a consequence of the steeper faint end and the absence of a pure exponential decline at the high-mass end; iii) the evolution of the comoving stellar mass density from z=0 to 5 can be modelled as log10 (rho_M) =-(0.05 +/- 0.09) z^2 - (0.22 -/+ 0.32) z + 8.69. At 3<=z<4, more than 30% of the M > 10^11 Msun galaxies would be missed by optical surveys with R<27 or z<26. Thus, our study demonstrates the importance of deep mid-IR surveys over large areas to perform a complete census of massive galaxies at high z and trace the early stages of massive galaxy assembly.
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