Oscillatory systems play an important role in the nature. Many engineering problems and physical systems of fifth degrees of freedom are oscillatory and their governing equations are fifth order nonlinear differential equations. To investigate the solution of fifth order weakly nonlinear oscillatory systems, in this article the Krylov–Bogoliubov–Mitropolskii (KBM) method has been extended and desired solution is found. An example is solved to illustrate the method. The results obtain by the extended KBM method show good agreement with those obtained by numerical method.