Angle-resolved photoemission spectroscopy (ARPES) has been used to study the electronic structure of InSe and CuIn5Se8 single crystals and determine the general patterns of its transformation after the introduction of copper. The main dispersion curves of valence bands in the studied multicomponent systems and the effective masses of majority carriers in CuIn5Se8 have been obtained. Joint theoretical and experimental research has allowed us to apply ARPES not only to single isolated states, but also to complex crystals with a large number of atoms in the unit cell (and, consequently, a large number of dispersion bands). It has been demonstrated that the neighborhoods of maxima and minima of dispersion curves E(k), which essentially define the set of experimental ARPES spectra, make the dominant contribution to the observed signal intensity.