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We present a new cubic theory of gravity in five dimensions which has secondorder traced field equations, analogous to BHT new massive gravity in threedimensions. Moreover, for static spherically symmetric spacetimes all the fieldequations are of second order, and the theory admits a new asymptoticallylocally flat black hole. Furthermore, we prove the uniqueness of this solution,study its thermodynamical properties, and show the existence of a C-functionfor the theory following the arguments of Anber and Kastor (arXiv:0802.1290[hep-th]) in pure Lovelock theories. Finally, we include theEinstein-Gauss-Bonnet and cosmological terms and we find new asymptotically AdSblack holes at the point where the three maximally symmetric solutions of thetheory coincide. These black holes may also possess a Cauchy horizon.

A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function