Abstract
Let A denote the mod 2 Steenrod algebra. In this thesis we determine the indecomposable elements in H^{5,*}(A)=Ext_A^{5,*}(Z/2,Z/2) by making calculations on the Ext groupsExt_A^{4,*}(\widetilde{H}^*(RP^\infty),Z/2) for the infinite real projective space RP^\infty. This together with the result of W. H. Lin on the decomposable elements in H^{5,*}(A) completely determine the structure of Ext_A^{5,*}(Z/2,Z/2)$.