  We continue the program, begun in \cite{gl3cpath}, to make a moonshine path
between a node of the extended $E_8$-diagram and the Monster simple group. Our
goal is to provide a context for observations of McKay, Glauberman and Norton
by realizing their theories in a more concrete form. In this article, we treat
the 5A-node. Most work in this article is a study of certain lattices of ranks
8, 16 and 24 whose determinants are powers of 5.
