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We derive a high-order nonlinear Schrödinger equation with fifth-order nonlinearity for the envelope of waves on the surface of a finite-depth irrotational, inviscid, and incompressible fluid over the flat bottom. This equation includes the fourth-order dispersion, cubic-quintic nonlinearity, and cubic nonlinear dispersion effects. The coefficients of this equation are given as functions of one dimensionless parameter kh, where k is the carrier wave number, and h is the undisturbed fluid depth. These coefficients stay bounded in the infinite-depth limit.

A Fifth-Order Nonlinear Schrödinger Equation for Waves on the Surface of Finite-Depth Fluid