We construct isospectral pairs of Riemannian metrics on S5 and on B6, thus lowering by three the minimal dimension of spheres and balls on which such metrics have been constructed previously (Sn≥8 and Bn≥9). We also construct continuous families of isospectral Riemannian metrics on S7 and on B8. In each of these examples, the metrics can be chosen equal to the standard metric outside certain subsets of arbitrarily small volume.
"Isospectral Metrics on Five-Dimensional Spheres." J. Differential Geom. 58 (1) 87 - 111, May, 2001. https://doi.org/10.4310/jdg/1090348283