This article’s aim is to investigate the fifth rank Sawada-kotera equation and get for approximate solution. Differential transform method was used, where the results were satisfactory and near to the optimal solution. A new hybrid modern was used between the numerical method and the hybrid algorithm hybrid gray Wolf and Cuckoo algorithm, where the approximate the shape of the solution of a polynomial and convergent series. Comparing the results with the exact solution shows the reliability of the hybrid technique and that the DTM method is an attractive, efficient and accurate method for solving systems of partial differential equations.