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We investigate the evolution of the H$\beta$+[OIII] and [OII] luminosityfunctions from $z \sim 0.8$ to $\sim5$ in four redshift slices per emissionline using data from the High-{\it z} Emission Line Survey (HiZELS). This isthe first time that the H$\beta$+[OIII] and [OII] luminosity functions havebeen studied at these redshifts in a self-consistent analysis. This is also thelargest sample of [OII] and H$\beta$+[OIII] emitters (3475 and 3298 emitters,respectively) in this redshift range, with large co-moving volumes $\sim 1\times 10^6$ Mpc$^{-3}$ in two independent volumes (COSMOS and UDS), greatlyreducing the effects of cosmic variance. The emitters were selected by acombination of photometric redshift and color-color selections, as well asspectroscopic follow-up, including recent spectroscopic observations usingDEIMOS and MOSFIRE on the Keck Telescopes and FMOS on Subaru. We find a strongincrease in $L_\star$ and a decrease in $\phi_\star$ for both H$\beta$+[OIII]and [OII] emitters. We derive the [OII] star-formation history of the Universesince $z\sim5$ and find that the cosmic SFRD rises from $z \sim 5$ to $\sim 3$and then drops towards $z \sim 0$. We also find that our star-formation historyis able to reproduce the evolution of the stellar mass density up to $z\sim 5$based only on a single tracer of star-formation. When comparing theH$\beta$+[OIII] SFRDs to the [OII] and H$\alpha$ SFRD measurements in theliterature, we find that there is a remarkable agreement, suggesting that theH$\beta$+[OIII] sample is dominated by star-forming galaxies at high-$z$ ratherthan AGNs.

Evolution of the H$\beta$+[OIII] and [OII] luminosity functions and the [OII] star-formation history of the Universe up to $z$ ~ 5 from HiZELS