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Multiple molecular lines are useful for studying the physical properties ofmultiphase star-forming gas in different types of galaxies. We probe themolecular gas throughout the disc of the spiral galaxy NGC~5033, hosting anactive galactic nucleus (AGN), using multiple low-$J$ CO lines [$^{12}$CO(1-0,2-1, 3-2 and $^{13}$CO(1-0, 2-1)] and dense gas tracers [HCN(1-0) andHCO$^{+}$(1-0)]. Firstly, we determine the ratios of the integrated intensitymaps and the ratio of intensities in position velocity diagrams. Secondly, weobtain the ratios of CO lines and high-density tracers at the centre; andthirdly, we model these line ratios using a radiative transfer code. Line ratiodiagnostics reveal that the south of the gaseous disc contains cooler gas thanthe northern part, and the centre hosts warmer and less tenuous gas with asimilar dense gas fraction compared to most galaxies of similar type. Our modelresults mostly agree with the empirical ones in the sense that the centralregion of NGC~5033 harbours warmer gas than that in the centres of normalspirals and lenticulars without showing AGN activity. Finally, thebeam-averaged total molecular gas mass and gas surface density along thegalaxy's major axis show a radial gradient, i.e. increasing from the outskirtsup to the central region of size $1$~kpc where there is a depression in bothgas mass and surface density.

Molecular line ratio diagnostics and gas kinematics in the AGN host Seyfert galaxy NGC 5033