The slow transition from an out-of-equilibrium glass towards a supercooled liquid is a complex relaxation phenomenon. In this Letter, we study the correlation between mechanical relaxation and equilibration kinetics in a Pd_{20}Pt_{20}Cu_{20}Ni_{20}P_{20} high-entropy metallic glass. The evolution of stress relaxation with aging time was obtained with an unprecedented detail, allowing us to pinpoint new interesting features. The long structural relaxation towards equilibrium contains a wide distribution of activation energies, instead of being just associated to the β relaxation as commonly accepted. The stress relaxation time can be correlated with the equilibration rate and we observe a decrease of microstructural heterogeneity which contrasts with an increase of dynamic heterogeneity. These results significantly enhance our insight of the interplay between relaxation dynamics and thermodynamics in metallic glasses.