Thanks to ALMA, observations of atomic fine-structure line emission are a very productive way of measuring physical properties of the interstellar-medium (ISM) in galaxies at high redshift. While the bright [CII] line has been abundantly exploited for dynamical studies of the gas, it needs to be compared to other lines in order to establish its physical origin. [NII] is selectively able to measure the emission coming from the ionized gas component. Thus, we here present ALMA measurements of [NII] 205 um fine-structure line emission from a representative sample of galaxies at z = 5–6 spanning two orders of magnitude in star-formation rate (SFR). Our results show at least two different regimes of ionized ISM properties for galaxies in the first billion years of cosmic time, separated by their L_[CII]/L_[NII] ratio. While we find extremely low [NII] emission compared to [CII] from a low-SFR typical galaxy (LBG-1), likely due to low dust content and reminiscent of local dwarfs; both the dusty Lyman Break Galaxy HZ10 and the extreme starburst AzTEC-3 interestingly show ionized-gas fractions typical of local star-forming galaxies and show hints of spatial variations in their [CII]/[NII] line ratio. These observations of a z > 5 sample of faint [NII] detections demonstrate how ALMA's unprecedented sensitivity to faint line emission can best constrain the ionized and neutral gas properties of galaxies over a large range in SFR and dust emission in the first billion years from normal star-forming galaxies, shedding light on some of the ISM properties that are most important to galaxy assembly through star formation.