  In a recent communication Nail Ibragimov introduced the concept of
nonlinearly self-adjoint differential equation [N. H. Ibragimov, Nonlinear
self-adjointness and conservation laws, J. Phys. A: Math. Theor., vol. 44,
432002, 8 pp., (2011)]. In the present communication a nonlinear self-adjoint
classification of a general class of fifth-order evolution equation with time
dependent coefficients is presented. As a result five subclasses of nonlinearly
self-adjoint equations of fifth-order and four subclasses of nonlinearly
self-adjoint equations of third-order are obtained. From the Ibragimov's
theorem on conservation laws [N. H. Ibragimov, A new conservation theorem, J.
Math. Anal. Appl., vol. 333, 311--328, (2007)] conservation laws for some of
these equations are established.
