jmc

Let $2x$ be the smaller integer. Then the larger integer is $5x$. The product of the integers is 160, so $(2x)(5x)=160⟹10x^2=160⟹x^2=16$. Since $x$ is positive, this implies $x=4$ which in turn implies that the larger integer is $5\cdot 4=\boxed{20}$.