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High entropy oxides (HEOx) are novel materials, which increase the potential application in the fields of energy and catalysis. However, a series of HEOx is too novel to evaluate the synthesis properties, including formation and fundamental properties. Combining first-principles calculations with machine learning (ML) techniques, we predict the lattice constants and formation energies of spinel-structured photocatalytic HEOx, (Co,Cr,Fe,Mn,Ni)₃O₄, for stoichiometric and non-stoichiometric structures. The effects of site occupation by different metal cations in the spinel structure are obtained through first-principles calculations and ML predictions. Our predicted results show that the lattice constants of these spinel-structured oxides are composition-dependent and that the formation energies of those oxides containing Cr atoms are low. The computing time and computing energy can be greatly economized through the tandem approach of first-principles calculations and ML.