SL(5) supersymmetry

We consider supersymmetry in five dimensions, where the fermionic parameters are a 2-form under SL(5). Supermultiplets are investigated using the pure spinor superfield formalism, and are found to be closely related to infinite-dimensional extensions of the supersymmetry algebra: the Borcherds superalgebra $\text{scr}B(E_4)$, the tensor hierarchy algebra $S(E_4)$ and the exceptional superalgebra $E(5,10)$. A theorem relating $\text{scr}B(E_4)$ and $E(5,10)$ to all levels is given.