Charged and Rotating Black Holes in $AdS_5 \times S^5$ are the dual description of  phases of N=4 Yang Mills theory (as a function of energy, angular momentum and charge). Familiar Kerr-Resiner Nordstorm AdS black holes dominate at high energies, but turn out to be unstable in a band of energies around extremality. We construct new black hole solutions that yield new phases that are the end point of this instability. These new phases dominate at low energies, and in particular in the BPS limit. We use our construction to provide a new conjecture for the supersymmetric cohomology of N=4 Yang Mills at large $N$, and discuss the interplay of our conjecture with field theory results for the superconformal Index.