  We show that theories having second-order field equations in the context of
higher-dimensional modified gravity are not restricted to the family of
Lovelock Lagrangians, but can also be obtained if no a priori assumption on the
relation between the metric and affine structures of space-time is made
(Palatini approach). We illustrate this fact by considering the case of
Palatini $f(R)$ gravities in five dimensions. Our results provide an
alternative avenue to explore new domains of the AdS/CFT correspondence without
resorting to {\it ad hoc} quasi-topological constructions.
