A set-theoretic solution of the Pentagon Equation on a non-empty set $S$ is a map $s:S^2to S^2$ such that $s_23s_13s_12=s_12s_23$, where $s_12=stimes id$, $s_23=idtimes s$ and $s_13=(τtimes id)(idtimes s)(τ times id)$ are mappings from $S^3$ to itself and $τ:S^2to S^2$ is the flip map, i.e., $τ(x,y)=(y,x)$. We give a description of all involutive solutions, i.e., $s^2=id$. It is shown that such solutions are determined by a factorization of $S$ as direct product $Xtimes Atimes G$ and a map $σ:Ato Sym(X)$, where $X$ is a non-empty set and $A$,$G$ are elementary abelian $2$-groups. Isomorphic solutions are determined by the cardinalities of $A$, $G$ and $X$, i.e., the map $σ$ is irrelevant. In particular, if $S$ is finite of cardinality $2^n(2m+1)$ for some $n,m≥ 0$ then, on $S$, there are precisely $binomn+22$ non-isomorphic solutions of the Pentagon Equation.