  We present ALMA detections of the [NII] 205$\mu$m and CO(12-11) emission
lines, and the tentative detection of [CI] $^3$P$_1$ - $^3$P$_0$ for the
strongly lensed ($\mu$=5.7$\pm$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 8.5 $\sigma$ level, respectively, by our band-6
observations. The [CI] line is detected at 3.2 $\sigma$ after a re-analysis of
existing band-3 data. The [CI] luminosity implies a gas mass of
3.8$\pm$1.2$\times$10$^{10}$ M$_\odot$, and consequently a very short depletion
timescale of 34$\pm$13 Myr and a CO-luminosity-to-gas-mass conversion factor
$\alpha_{\rm CO}$ of 1.0$\pm$0.3 M$_\odot$ (K km s$^{-1}$ pc$^{2}$)$^{-1}$.
SPT2132-58 is an extreme starburst with an intrinsic star formation rate of
1100$\pm$200 M$_\odot$/yr. We find a [CII]/[NII] ratio of 26$\pm$7, which is
the highest reported at z$>$4. This suggests that SPT2132-58 hosts an evolved
interstellar medium (0.5 Z$_\odot$<Z<1.5 Z$_\odot$), 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 AGN.
