Spectra of luminescence and magnetic circular polarization of luminescence corresponding to the 5D4̊→ 7F5 radiative transition of the Tb3+ ion in an yttrium-aluminum garnet are studied experimentally. In the context of crystalline field theory, the energy spectrum of the 7F5 multiplet of the Tb3+ ion in the garnet is calculated. The structure of internal energy levels of the 7F5 multiplet of the Tb3+ ion is refined based on a comparison of the calculated results with the experimental data, and the diagram of magnetooptically active radiating transitions between 5D4 and 7F5 multiplet energy sublevels is constructed.