Determination of \(\mathrm{Ext}^{5,*}_{\mathcal A}(\mathbb Z/2,\mathbb Z/2)\) (Q629726)

Let \({\mathcal A}\) be the mod 2 Steenrod algebra. The Ext groups \(\text{Ext}^{s,t}_{\mathcal A} (\mathbb Z/2,\mathbb Z/2)\) form the \(E_2\)-term of the Adams spectral sequence for computing the stable homotopy groups of spheres. The computation of \(\text{Ext}^{s,t}_{\mathcal A}\) is a classical problem in homotopy theory. The groups \(\text{Ext}^{s,*}_{\mathcal A}\) have been previously determined for \(s\leq 4\) as well as the decomposable elements in the terms \(\text{Ext}^{5,*}_{\mathcal A}\). In this article, the author determines the indecomposable elements in the terms \(\text{Ext}^{5,*}_{\mathcal A}\) based on a lot of hard computations using the program developed by W. H. Lin. Together with the work of Lin on the decomposable elements, this completely determines the terms \(\text{Ext}^{5,*}_{\mathcal A}\).