  We construct isospectral pairs of Riemannian metrics on S^5 and on B^6, thus
lowering by three the dimension of spheres and balls on which such metrics have
been constructed previously (S^{n\ge 8} and B^{n\ge 9}). We also construct
continuous families of isospectral Riemannian metrics on S^7 and on B^8. In
each of these examples, the metrics can be chosen equal to the standard metric
outside certain subsets of arbitrarily small volume.
