The magnetization and sound propagation in single-crystalline ErFe ₅Al₇ (tetragonal crystal structure) have been studied in steady (up to 18 T) and pulsed magnetic fields (up to 60 T). The compound orders ferrimagnetically at a Curie temperature T_C=201 K and has a compensation point at T_comp=34 K. ErFe₅Al₇ displays a strong magnetic easy-plane anisotropy. A strong magnetic anisotropy is present as well within the basal plane; the [100] axis is the easy magnetization direction with a spontaneous magnetic moment M_s=1.3 μ_B/f.u. at 2 K. Field-induced magnetic transitions, two along the [100] axis and two along the [110] axis, have been found in the vicinity of T=T_comp. Changes in the magnetic state at the transitions result in significant alterations of the spin-phonon coupling, which is manifested by sharp anomalies in the sound velocity and sound attenuation. Along the easy [100] axis the forced ferromagnetic state is reached in a field of about 50 T at 2 K, whereas along the [110] direction saturation is expected only above 60 T. A magnetic field-temperature phase diagram has been extracted up to 60 T. From the experimental data a value of n_ErFe=3.3 T/μ_B for the inter-sublattice Er-Fe exchange interaction has been obtained.