Charting the main sequence of star-forming galaxies out to redshifts z~<5.7

We present a new determination of the star-forming main sequence (MS), obtained through stacking 100k K-band-selected galaxies in the far-infrared (FIR) Herschel and James Clerk Maxwell Telescope (JCMT) imaging. By fitting the dust emission curve to the stacked FIR photometry, we derive the IR luminosities (L_ IR), and hence the star formation rates (SFRs) out to z 5. 7. The functional form of the MS is found, with the linear SFR-M_ relation that flattens at high stellar masses and the normalization that increases exponentially with redshift. We derive the corresponding redshift evolution of the specific star formation rate (sSFR) and compare our findings with the recent literature. We find our MS to be exhibiting slightly lower normalization at z 2 and to flatten at somewhat larger stellar masses at high redshifts. By deriving the relationship between the peak dust temperature d) and redshift, where T_ d increases linearly from 20\, K at z=0. 5 to 50\, K at z=5, we conclude that the apparent inconsistencies in the shapes of the MS are most likely caused by the different dust temperatures assumed when deriving SFRs in the absence of FIR data. Finally, we investigate the derived shape of the star-forming MS by simulating the time evolution of the observed galaxy stellar mass function (GSMF). While the simulated GSMF is in good agreement with the observed one, some inconsistencies persist. In particular, we find the simulated GSMF to be slightly overpredicting the number density of low-mass galaxies at z