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Abstract We develop the analysis of the asymptotic properties of gravity in higher spacetime dimensions D, with a particular emphasis on the case D = 5. Our approach deals with spatial infinity and is Hamiltonian throughout. It is shown that the asymptotic symmetry algebra BMS5, which is realized non linearly, contains a four-fold family of angle- dependent supertranslations. The structure of this non-linear algebra is investigated and a presentation in which the Poincaré subalgebra is linearly realized is constructed. Invariance of the energy is studied. Concluding comments on higher dimensions D ≥ 6 are also given.