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 _ { 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 6 , 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 .