Anti-de Sitter space with identified points give rise to black-hole structures. This was first pointed out in three dimensions and generalized to higher dimensions by Aminneborg et al. In this paper, we analyse several aspects of the five-dimensional anti-de Sitter black hole, including its relation to thermal anti-de Sitter space, its embedding in a Chern - Simons supergravity theory, its global charges and holonomies and the existence of Killing spinors.