We report interferometric imaging of [ C II ] ( ^ { 2 } P _ { 3 / 2 } \to ^ { 2 } P _ { 1 / 2 } ) and OH ( ^ { 2 } \Pi _ { 1 / 2 } J =3/2 \to 1/2 ) emission toward the center of the galaxy protocluster associated with the z =5.3 submillimeter galaxy ( SMG ) AzTEC-3 , using the Atacama Large ( sub ) Millimeter Array ( ALMA ) . We detect strong [ C II ] , OH , and rest-frame 157.7 \mu m continuum emission toward the SMG . The [ C II ] ( ^ { 2 } P _ { 3 / 2 } \to ^ { 2 } P _ { 1 / 2 } ) emission is distributed over a scale of 3.9 kpc , implying a dynamical mass of 9.7 \times 10 ^ { 10 } M _ { \odot } , and a star formation rate ( SFR ) surface density of \Sigma _ { SFR } =530 M _ { \odot } yr ^ { -1 } kpc ^ { -2 } . This suggests that AzTEC-3 forms stars at \Sigma _ { SFR } approaching the Eddington limit for radiation pressure supported disks . We find that the OH emission is slightly blueshifted relative to the [ C II ] line , which may indicate a molecular outflow associated with the peak phase of the starburst . We also detect and dynamically resolve [ C II ] ( ^ { 2 } P _ { 3 / 2 } \to ^ { 2 } P _ { 1 / 2 } ) emission over a scale of 7.5 kpc toward a triplet of Lyman-break galaxies with moderate UV-based SFRs in the protocluster at \sim 95 kpc projected distance from the SMG . These galaxies are not detected in the continuum , suggesting far-infrared SFRs of < 18–54 M _ { \odot } yr ^ { -1 } , consistent with a UV-based estimate of 22 M _ { \odot } yr ^ { -1 } . The spectral energy distribution of these galaxies is inconsistent with nearby spiral and starburst galaxies , but resembles those of dwarf galaxies . This is consistent with expectations for young starbursts without significant older stellar populations . This suggests that these galaxies are significantly metal-enriched , but not heavily dust-obscured , “ normal ” star-forming galaxies at z > 5 , showing that ALMA can detect the interstellar medium in “ typical ” galaxies in the very early universe .