  In this paper, we classify and construct five-dimensional black holes on
gravitational instantons in vacuum Einstein gravity, with RxU(1)xU(1) isometry.
These black holes have spatial backgrounds which are Ricci-flat gravitational
instantons with U(1)xU(1) isometry, and are completely regular space-times
outside the event horizon. Most of the known exact five-dimensional vacuum
black-hole solutions can be classified within this scheme. Amongst the new
space-times presented are static black holes on the Euclidean Kerr and
Taub-bolt instantons. We also present a rotating black hole on the
Eguchi-Hanson instanton.
