  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 BMS$_5$, 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
Poincar\'e subalgebra is linearly realized is constructed. Invariance of the
energy is studied. Concluding comments on higher dimensions $D \geq 6$ are also
given.
