  Generalized parallelizable spaces allow a unified treatment of consistent
maximally supersymmetric truncations of ten- and eleven-dimensional
supergravity in generalized geometry. Known examples are spheres, twisted tori
and hyperboloides. They admit a generalized frame field over the coset space
$M$=$G/H$ which reproduces the Lie algebra $\mathfrak{g}$ of $G$ under the
generalized Lie derivative. An open problem is a systematic construction of
these spaces and especially their generalized frames fields. We present a
technique which applies to $\dim M$=4 for SL(5) exceptional field theory. In
this paper the group manifold $G$ is identified with the extended space of the
exceptional field theory. Subsequently, the section condition is solved to
remove unphysical directions from the extended space. Finally, a SL(5)
generalized frame field is constructed from parts of the left-invariant
Maurer-Cartan form on $G$. All these steps impose conditions on $G$ and $H$.
