We establish a robust statistical description of the star-forming galaxy population at the end of cosmic HI reionization ($5.0le{}zle6.6$) from a large sample of 52 galaxies with spectroscopically confirmed redshifts from the VIMOS UltraDeep Survey. We identify galaxies with Ly$alpha$ either in absorption or in emission, at variance with most spectroscopic samples in the literature where Ly$alpha$ emitters dominate. We find that star-forming galaxies at these redshifts are distributed along a main sequence in the stellar mass vs. SFR plane. We report a flat evolution of the sSFR(z) in 3<z<6 compared to lower redshift measurements. UV-continuum slopes vary with luminosity, with a large dispersion. We determing UV and Ly$alpha$ luminosity functions using V$_{max}$ method and use them to derive star formation rate densities (SFRD). We find that both UV-derived and Ly$alpha$-derived SFRDs are in excellent agreement after correcting Ly$alpha$ luminosity density for IGM absorption. Our new SFRD measurements at a mean redshift z=5.6 confirm the steep decline of the SFRD at z>2. The bright end of the Ly$alpha$ luminosity function has a high number density, indicating a significant star formation activity concentrated in the brightest Ly$alpha$ emitters (LAE) at these redshifts. LAE with EW>25AA ~contribute to about 75% of the total UV-derived SFRD. While our analysis favors a low dust content in 5.0<z<6.6, uncertainties on the dust extinction correction and associated degeneracies in spectral fitting will remain an issue to estimate the total SFRD until future survey extending spectroscopy to the NIR rest-frame spectral domain, e.g. with JWST.
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