We shall identify the conditions under which there is near-horizon supersymmetry enhancement for supersymmetric black hole solutions to minimal five dimensional gauged supergravity. As all known black holes of the gauged theory exhibit supersymmetry enhancement from 1/4 to 1/2 in the near horizon limit, it is natural to investigate if this is generic. A further motivation is that one can demonstrate, assuming supersymmetry enhancement, the existence of two commuting rotational isometries of the full solution. And it is known that under this latter condition there are no asymptotically AdS supersymmetric black ring solutions with regular horizons.