  In this article we give a full description of the dynamics of the flat
anisotropic (4+1)-dimensional cosmological model in the presence of both
Gauss-Bonnet and Einstein contributions. This is the first complete description
of this model with both terms taken into account. Our data is obtained using
the numerical analysis, though, we use analytics to explain some features of
the results obtained, and the same analytics could be applied to
higher-dimensional models in higher-order Lovelock corrections. Firstly, we
investigate the vacuum model and give a description of all regimes; then, we
add a matter source in the form of perfect fluid and study the influence the
matter exerts upon the dynamics. Thus, we give a description of matter regimes
as well. Additionally, we demonstrate that the presence of matter not only
"improves" the situation with a smooth transition between the standard
singularity and the Kasner regime, but also brings additional regimes and even
partially "erases" the boundaries between different regimes inside the same
triplet. Finally, we discuss the numerical and analytical results obtained and
their generalization to the higher-order models.
