We have obtained deep 1 and 3 mm spectral-line scans towards a candidate z ≳ 5 ALMA-identified AzTEC submillimetre galaxy (SMG) in the Subaru/XMM-Newton Deep Field (or UKIDSS UDS), ASXDF1100.053.1, using the NOrthern Extended Millimeter Array (NOEMA), aiming to obtain its spectroscopic redshift. ASXDF1100.053.1 is an unlensed optically dark millimetre-bright SMG with S 1100 μ m = 3:5 mJy and KAB > 25:7 (2s), which was expected to lie at z = 5-7 based on its radio-submillimetre photometric redshift. Our NOEMA spectral scan detected line emission due to 12CO(J = 5-4) and (J = 6-5), providing a robust spectroscopic redshift, zCO = 5:2383 ± 0:0005. Energy-coupled spectral energy distribution modelling from optical to radio wavelengths indicates an infrared luminosity LIR = 8:3+1:5-1:4 × 1012 L, a star formation rate SFR = 630+-260 380 M yr-1, a dust mass Md = 4:4+-0 0:4 3 × 108 M, a stellar mass Mstellar = 3:5+3:6-1:4 × 1011 M, and a dust temperature Td = 37:4+-2 1:3 8 K. The CO luminosity allows us to estimate a gas mass M gas = 3:1 ± 0:3 × 1010 M, suggesting a gas-to-dust mass ratio of around 70, fairly typical for z ∼ 2 SMGs. ASXDF1100.053.1 has ALMA continuum size Re = 1:0+0:2-0:1 kpc, so its surface infrared luminosity density SIR is 1:2+-0 0:1 2 × 1012 L kpc-2. These physical properties indicate that ASXDF1100.053.1 is a massive dusty star-forming galaxy with an unusually compact starburst. It lies close to the star-forming main sequence at z ∼ 5, with low Mgas/Mstellar = 0:09, SFR/SFRMS(RSB) = 0:6, and a gas-depletion time tdep of 50 Myr, modulo assumptions about the stellar initial mass function in such objects. ASXDF1100.053.1 has extreme values of M gas=Mstellar, RSB, and tdep compared to SMGs at z ∼ 2-4, and those of ASXDF1100.053.1 are the smallest among SMGs at z > 5. ASXDF1100.053.1 is likely a late-stage dusty starburst prior to passivisation. The number of z = 5:1-5.3 unlensed SMGs now suggests a number density dN=dz = 30:4 ± 19:0 deg-2, barely consistent with the latest cosmological simulations.