Determination of

Let A denote the mod 2 Steenrod algebra. In this paper we determine the indecomposable elements in H 5 , ⁎ ( A ) = Ext A 5 , ⁎ ( Z / 2 , Z / 2 ) by making calculations on the Ext groups Ext A 4 , ⁎ ( H ˜ ⁎ ( R P ∞ ) , Z / 2 ) for the infinite real projective space R P ∞ . 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 ) .