homework and exercises - 5D Ricci Curvature

As part of a hw problem for a class, we're supposed to be deriving the equivalence given in equation 2.3 of this paper http://arxiv.org/abs/1107.5563. I was wondering if there is some special relation involving the Ricci Curvature in 5d's relationship to one in 4d. Since with a general metric like the one given in 2.1, calculating the Christoffel symbols would seem to be an enormous and not particularly smart idea.