  Using exceptional generalised geometry, we classify which five-dimensional
${\cal N}=2$ gauged supergravities can arise as a consistent truncation of
10-/11-dimensional supergravity. Exceptional generalised geometry turns the
classification into an algebraic problem of finding subgroups $G_S \subset
\mathrm{USp}(8) \subset \mathrm{E}_{6(6)}$ that preserve exactly two spinors.
Moreover, the intrinsic torsion of the $G_S$ structure must contain only
constant singlets under $G_S$, and these, in turn, determine the gauging of the
five-dimensional theory. The resulting five-dimensional theories are strongly
constrained: their scalar manifolds are necessarily symmetric spaces and only a
small number of matter multiplets can be kept, which we completely enumerate.
We also determine the largest reductive and compact gaugings that can arise
from consistent truncations.
