  A fifth-order KdV equation with time dependent coefficients and linear
damping has been studied. Symmetry groups have several different applications
in the context of nonlinear differential equations. For instance, they can be
used to determine conservation laws. We obtain the symmetries of the model
applying Lie's classical method. The choice of some arbitrary functions of the
equation by the equivalence transformation enhances the study of Lie symmetries
of the equation. We have determined the subclasses of the equation which are
nonlinearly self-adjoint. This allow us to obtain conservation laws by using a
theorem proved by Ibragimov which is based on the concept of adjoint equation
for nonlinear differential equations.
