On a minimal set of generators for the polynomial algebra of five variables as a module over the Steenrod algebra

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Denote by Pₖ the graded polynomial algebra F₂[x₁,x₂,,xₖ] over the prime field of two elements, F₂, with the degree of each xᵢ being 1. We study the Peterson hit problem of determining a minimal set of generators for Pₖ as a module over the mod-2 Steenrod algebra, A. In this paper, we explicitly determine a minimal set of A-generators for Pₖ in the case k=5 and the degree 4(2ᵈ - 1) with d an arbitrary positive integer.