The aim of this paper is to give an alternative proof of a theorem about the
existence of contact structures on five-manifolds due to Geiges. This theorem
asserts that simply-connected five-manifolds admit a contact structure in every
homotopy class of almost contact structures. Our proof uses the open book
construction of Giroux.Comment: 15 pages, 2 figures; typos corrected, used simpler argument for
section 3; to appear in Annales de l'institut Fourie
