  A comprehensive analysis is presented based exclusively on near-horizon data
to determine the attractor equations and the entropy of BPS black holes and
rings in five space-time dimensions, for a Lagrangian invariant under eight
supersymmetries with higher-derivative couplings. For spinning black holes the
results only partially agree with the results of previous work, where often
additional input was used beyond the near-horizon behaviour. A number of
discrepancies remains, for example, pertaining to small black holes and to
large spinning black holes, which are related to the presence of the
higher-derivative couplings. Arguments are presented to explain some of them.
For the black rings, the analysis is intricate due to the presence of
Chern-Simons terms and due to the fact that the gauge fields are not globally
defined. The contributions from the higher-derivative couplings take a
systematic form in line with expectations based on a variety of arguments.
