Tensor invariants of fifth-order dynamical systems with dissipation

New cases of integrable dynamical systems of the fifth-order homogeneous in terms of variables are presented, in which a system on a tangent bundle to a two-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has a dissipation of different signs. The external field is introduced using some unimodular transformation and generalizes the previously considered fields. Complete sets of both the first integrals and invariant differential forms are given.