In this work, we present the results of the thermodynamic assessment of two equiatomic refractory High Entropy Alloys (HEAs), namely TaMoCrTiAl and NbMoCrTiAl, in the temperature range between 700 and 1500°C. Particular attention is paid on the constitution of the intermetallic phases stable in these alloy systems. Thermodynamic calculations were performed using a self-developed thermodynamic database based on the CALPHAD (Calculation of Phase Diagram) approach. The details of the thermodynamic modelling and particular characteristics of the relevant phases within the Ta-Nb-Cr-Ti-Al system are presented. To verify the new database, the phase formation and stability of both quinary alloys in near-equilibrium conditions were studied experimentally by utilizing scanning electron microscopy (SEM) with energy dispersive spectroscopy (EDS) and electron backscatter diffraction (EBSD) as well as X-ray powder diffraction (XRD). Both equiatomic alloys reveal a complex microstructure including several intermetallic phases at intermediate temperatures. The alloy NbMoCrTiAl consists of an ordered B2 phase, Al(Mo, Nb)3 and two polytypes (C14 and C15) of the Cr2Nb Laves phase. Precipitations of Cr2Ta Laves phase (C14, C15 and C36-type) in the B2 matrix were observed in the alloy TaMoCrTiAl. Based on the results of thermodynamic calculations, it was concluded that: (i) Nb stabilizes the AlMo3 A15 phase in the alloy NbMoCrTiAl, (ii) Al and Ti play a crucial role in the formation of the ordered B2 phase in both alloys and (iii) the concentrations of Cr and/or Ta/Nb should be dramatically reduced to decrease the Laves phase volume fraction.