Based on the deep understanding of χ ( 2 ) cascading nonlinearity, a configuration of phase-mismatched frequency tripling is proposed to produce high-order nonlinear phase shifts. In this process, induced effective fifth-order nonlinearity dominates, which is proportional to the square of input fundamental intensity in the limits of large phase-mismatch and negligible pump depletion in the first crystal. Compared with the conventional induced effective third-order nonlinearity, theoretical study and numerical simulations show that the induced fifth-order nonlinear phase shifts can be much larger in magnitude with a controllable sign and a richer saturable feature.