We show that almost all extremal black holes in Einstein-Maxwell-AdS theory develop diverging tidal forces at the horizon. This singularity in five (and higher) dimensions implies that the near horizon geometry of extreme Reissner-Nordstrom-AdS black holes are RG unstable under small changes of the boundary conditions at infinity. We found an infinite number of new one-parameter families of static extremal horizons. Their cross-sections are highly deformed three-spheres with an $SO(3)$ symmetry group. Numerical simulations show that generic boundary conditions at infinity lead to horizons belonging to a particular one-parameter family. Thus, this particular family is dual to new IR fixed points for the dual gauge theory. These fixed points seem to be stable under the RG flow, in contrast with the usual spherically symmetric ones.