  According to Giroux, contact manifolds can be described as open books whose
pages are Stein manifolds. For 5-dimensional contact manifolds the pages are
Stein surfaces, which permit a description via Kirby diagrams. We introduce
handle moves on such diagrams that do not change the corresponding contact
manifold. As an application, we derive classification results for subcritically
Stein fillable contact 5-manifolds and characterise the standard contact
structure on the 5-sphere in terms of such fillings. This characterisation is
discussed in the context of the Andrews-Curtis conjecture concerning
presentations of the trivial group. We further illustrate the use of such
diagrams by a covering theorem for simply connected spin 5-manifolds and a new
existence proof for contact structures on simply connected 5-manifolds.
