Atomic-scale simulations and modelling were carried out to investigate the thermodynamic properties of the bcc AlCrFeMnMo equiatomic high-entropy alloy (HEA) solid solution. Special care was taken to the determination of elemental chemical potentials, which are the central quantities governing the behaviour of HEAs in practical situations. The statistical properties of the disordered alloy were studied by extensive use of special quasirandom structures, including the influence of various types of short-range order. The local atomic order in AlCrFeMnMo appears to promote pairs of unlike atoms, although such non-random atomic arrangements are at odds with commonly admitted pictures for HEAs. While the chemical potentials derived from our moderate-size (~1000 alloy configurations) statistical sample reveal an overall agreement on trends, more quantitative estimations of these quantities remain tricky. A significant (~0.5 eV) uncertainty should be taken into account when using chemical potentials in further studies involving HEA solid solutions in equilibrium with other phases.