  We explore the build-up of stellar mass in galaxies over a wide redshift
range 0.4 < z < 5.0 by studying the evolution of the specific star formation
rate (SSFR), defined as the star formation rate per unit stellar mass, as a
function of stellar mass and age. Our work is based on a combined sample of ~
9000 galaxies from the FORS Deep Field and the GOODS-S field, providing high
statistical accuracy and relative insensitivity against cosmic variance. As at
lower redshifts, we find that lower-mass galaxies show higher SSFRs than higher
mass galaxies, although highly obscured galaxies remain undetected in our
sample. Furthermore, the highest mass galaxies contain the oldest stellar
populations at all redshifts, in principle agreement with the existence of
evolved, massive galaxies at 1 < z < 3. It is remarkable, however, that this
trend continues to very high redshifts of z ~ 4. We also show that with
increasing redshift the SSFR for massive galaxies increases by a factor of ~
10, reaching the era of their formation at z ~ 2 and beyond. These findings can
be interpreted as evidence for an early epoch of star formation in the most
massive galaxies, and ongoing star-formation activity in lower mass galaxies.
