<p>The fifth-order Korteweg-de Vries (KdV) equation is a nonlinear partial differential equation that describes wave propagation in shallow water waves and other nonlinear wave phenomena. In this paper, we present numerical solutions of a generalized fifth-order KdV initial-boundary value problem using the shifted Legendre collocation method. The method assumes that the solution of the proposed problem can be expressed as a double shifted Legendre polynomial series, with constant expansion coefficients to be determined. Using the zeros of shifted Legendre polynomials as collocation points, the proposed problem is transformed into a set of nonlinear algebraic equations in the constant expansion coefficients. These algebraic equations are then solved using Newton’s iteration method. A convergence analysis of the proposed method is presented. The proposed collocation method is implemented on six special cases of the generalized fifth-order KdV equations—Lax equation, Sawada-Kotera equation, Caudrey-Dodd-Gibbon equation, Kaup-Kuperschmidt equation, and Ito equation, as illustrative examples. Comparisons of the obtained approximate solutions with exact solutions and other existing results are demonstrated in tables and graphs. The comparative analysis shows that the proposed method yields higher accuracy compared to the existing methods.</p>