  We show how to construct seven-dimensional half-maximally supersymmetric
consistent truncations of 11-/10-dimensional SUGRA using $\mathrm{SL}(5)$
exceptional field theory. Such truncations are defined on generalised
$\mathrm{SU}(2)$-structure manifolds and give rise to seven-dimensional
half-maximal gauged supergravities coupled to $n$ vector multiplets and thus
with scalar coset space $\mathbb{R}^+ \times
\mathrm{O}(3,n)/\mathrm{O}(3)\times\mathrm{O}(n)$. The consistency conditions
for the truncation can be written in terms of the generalised Lie derivative
and take a simple geometric form. We show that after imposing certain "doublet"
and "closure" conditions, the embedding tensor of the gauged supergravity is
given by the intrinsic torsion of generalised $\mathrm{SU}(2)$-connections and
automatically satisfies the linear constraint of seven-dimensional half-maximal
gauged supergravities, as well as the quadratic constraint when the section
condition is satisfied.
