We report interferometric measurements of [NII] 205 um fine-structure line emission from a representative sample of three galaxies at z=5-6 using the Atacama Large (sub)Millimeter Array (ALMA). These galaxies were previously detected in [CII] and far-infrared continuum emission and span almost two orders of magnitude in star formation rate (SFR). Our results show at least two different regimes of ionized inter-stellar medium properties for galaxies in the first billion years of cosmic time, separated by their L_[CII]/L_[NII] ratio. We find extremely low [NII] emission compared to [CII] (L_ [CII]/L_[NII]=68 [+200/-28]) from a typical L*_UV star-forming galaxy, likely directly or indirectly (by its effect on the radiation field) related to low dust abundance and low metallicity. The infrared-luminous modestly star-forming Lyman Break Galaxy (LBG) in our sample is characterized by an ionized-gas fraction (L_[CII]/L_[NII]<=20) typical of local star-forming galaxies and shows evidence for spatial variations in its ionized-gas fraction across an extended gas reservoir. The extreme SFR, warm and compact dusty starburst AzTEC-3 shows an ionized fraction higher than expected given its star-formation rate surface density (L_[CII]/L_[NII]=22+/-8) suggesting that [NII] dominantly traces a diffuse ionized medium rather than star-forming HII regions in this type of galaxy. This highest redshift sample of [NII] detections provides some of the first constraints on ionized and neutral gas modeling attempts and on the structure of the inter-stellar medium at z=5-6 in normal galaxies and starbursts.
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