Theoretically predicted and experimentally confirmed occurrence of infrared-induced second harmonic generation for glasses in the middle infrared spectral region is described by fifth-order nonlinear optical susceptibility. This effect is observed in the middle-IR region when the value of the electronic energy gap is comparable to the energies of actual phonons participating in the anharmonic (noncentrosymmetric) electron-phonon interactions. As a subject for the investigations, Sb2Te3-BaF2-PbCl2 glasses were chosen because they are transparent in the spectral range of 0.8-10.1 mum. The second harmonic generation (SHG) output signal within the 1.5-4.8 mum spectral range demonstrated a significant spectral dependence. Correlation of the SHG spectral dependences with spectral positions of the anharmonic phonon frequencies confirms that the fifth-order steady-state process occurs as a result of both the cascading processes and IR-induced charge density noncentrosymmetry. A maximum value of the SHG is achieved at a pump-probe delay time of about 20 ps, which is typical for the anharmonic electron-phonon interactions.