On a minimal set of generators for the polynomial algebra of five variables in a generic degree

Let [Formula: see text] be the graded polynomial algebra [Formula: see text] over the prime field of two elements, [Formula: see text], with the degree of each [Formula: see text] being 1. We study the hit problem, set up by Frank Peterson, of finding a minimal set of generators for [Formula: see text] as a module over the mod-[Formula: see text] Steenrod algebra, [Formula: see text] It is an open problem in Algebraic Topology. In this paper, we explicitly determine a minimal set of [Formula: see text]-generators for [Formula: see text] in the case of the generic degrees [Formula: see text] for all [Formula: see text].