We study the hit problem, set up by F. Peterson of finding a minimal set of generators for the polynomial algebra
as a module over the mod-2 Steenrod algebra, A. By assigning degree 1 to each
is regarded as a graded algebra over the ground field F2
. The mod 2 cohomology ring of the k-fold Cartesian product of infinite dimensional real projective spaces is isomorphic to Pk
as a graded algebra. Through this isomorphism, we may regard Pk
as an A-module where A stands for the mod 2 Steenrod algebra. In this paper, we explicitly determine the hit problem for the case of k=5 in degree 8 in terms of the admissible monomials.