"We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) spacetime by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS spacetime is unstable under arbitrarily small generic perturbations."
Piotr Bizoń, Andrzej Rostworowski
Notice that this study was done in 3+1 dimensional AdS4, but the authors claim (in the conclusion) that they observed "qualitatively the same behavior" for the 4+1 dimensional AdS5.
But with all the activity about AdS/CFT, it is it hard to believe that nobody checked the stability of AdS in classical GR before.