Geometry and fluxes of SL(5) exceptional field theory

We use a geometric approach to construct a flux formulation for the SL(5) U-duality manifest exceptional field theory. The resulting formalism is well-suited for studying gauged supergravities with geometric and non-geometric fluxes. Here we describe all such fluxes for both M-theory and IIB supergravity including the Ramond-Ramond fields for compactifications to seven dimensions. We define the locally non-geometric "R-flux" and globally non-geometric "Q-flux" for M-theory and find a new locally non-geometric R-flux for the IIB theory. We show how these non-geometric fluxes can be understood geometrically and give some examples of how they fluxes can be generated by acting with dualities on solutions with geometric or field-strength flux.