  We consider the five-dimensional Einstein-Gauss-Bonnet gravity, which can be
obtained by means of an apropriate choice of coeficients in the
five-dimensional Lanczos-Lovelock gravity theory. The Einstein-Gauss-Bonnet
field equations for the Friedmann-Lema\^itre-Robertson-Walker metric are found
as well as some of their solutions. A four-dimensional gravity action is
obtained from the Gauss-Bonnet gravity using the Randall-Sundrum
compactification procedure and then it is studied the implications of the
compactification procedure in the cosmological solutions. The same procedure is
used to obtain gravity in four dimensions from the five-dimensional
AdS-Chern-Simons gravity to then study some cosmological solutions. The same
procedure is used to obtain gravity in 4D from the five-dimensional
AdS-Chern-Simons gravity to then study some cosmological solutions. Some
aspects of the construction of the four-dimensional action gravity are
considered in an Appendix.
