  We classify closed, simply-connected non-negatively curved 5-manifolds
admitting an (almost) effective, isometric $T^3$ or $T^2$ action. As a direct
consequence, we show that for any manifold, of dimensions up to and including 9
under the same hypotheses, the maximal symmetry rank is equal to $[2n/3]$ and
the free rank is less than or equal to one half that value.
