We show that a spin-5/2 field can be consistently coupled to gravitation without cosmological constant in five-dimensional spacetimes. The fermionic gauge "hypersymmetry" requires the presence of a finite number of additional fields, including a couple of U(1) fields, a spinorial two-form, the dual of the graviton (of mixed (2,1) Young symmetry) and a spin-3 field. The gravitational sector of the action is described by the purely quadratic Gauss-Bonnet term, so that the field equations for the metric are of second order. The local gauge symmetries of the full action principle close, without the need of auxiliary fields, for a suitable extension of the "hyper-Poincare" algebra. Apart from the Poincare and spin-3/2 generators, it includes a generator of spin 2 and a U(1) central extension. Noteworthy, the algebra admits an invariant trilinear form, and its generators allow us to precisely accommodate the entire field content within a single connection, so that the hypergravity action can be formulated as a gauge theory described by a Chern-Simons form in five dimensions.