We present ALMA detections of the [NII] 205 μm and CO(12-11) emission lines, and the tentative detection of [CI] - for the strongly lensed (μ = 5.7 ± 0.5) dusty, star-forming galaxy SPT-S J213242-5802.9 (hereafter SPT2132-58) at z = 4.77. The [NII] and CO(12-11) lines are detected at 11.5 and 8.5σ levels, respectively, by our band 6 observations. The [CI] line is detected at 3.2σ after a reanalysis of existing band 3 data. The [CI] luminosity implies a gas mass of (3.8 ± 1.2) × 1010M⊙, and, consequently, a very short depletion timescale of 34 ± 13 Myr and a CO luminosity to gas mass conversion factor αCO of 1.0 ± 0.3 M⊙ (K km s-1 pc2)-1. SPT2132-58 is an extreme starburst with an intrinsic star formation rate of 1100 ± 200 M⊙/yr. We find a [CII]/[NII] ratio of 26 ± 6, which is the highest ratio reported at z > 4. This suggests that SPT2132-58 hosts an evolved interstellar medium (0.5 Z⊙⊙), which may be dominated by photodissociation regions. The CO(2-1) and CO(5-4) transitions have lower CO to far-infrared ratios than local and high-redshift samples, while CO(12-11) is similar to these samples, suggesting the presence of an additional very excited component or an active galactic nucleus.
