Current constraints on the [CII] luminosity function at z ∼ 4.5 (upper panel) and z ∼ 5.5 (lower panel), and comparison with our SIDES simulation. The filled blue (z ∼ 4.5) and red (z ∼ 5.5) rectangles show the reconstruction of the luminosity function from the ALPINE sample (Yan et al. 2020). The two data points at the lowest luminosities could be impacted by non-detections and the upper limits estimated by Yan et al. (2020) are shown as downward arrows. The constraint at z ∼ 5 using the other sideband of ALPINE is shown with green rectangles (Loiacono et al. 2021). The solid red lines and the dashed orange lines are the SIDES results, assuming the DL14 or the L18 relation, respectively. The long-dashed brown line is the flat high-z SFRD version of SIDES.