Supersymmetry enhancement at the horizon of BPS black holes and rings in five space-time dimensions with eight supersymmetries, imposes stringent conditions on the fields and the geometry. For example, the BPS near-horizon geometry follows irrespective of the details of the Lagrangian. From the horizon behaviour alone the entropy and the attractor equations are derived. For spinning black holes, the results only partially agree with previous work, where additional input was used beyond the near-horizon data. In particular, the results fail to agree with four-dimensional results in the presence of higher-derivative interactions. Arguments are presented for this discrepancy. For the black rings, the horizon behavior leads to results which are consistent with the four-dimensional case, although subtle issues remain.