  In a previous paper, the potential automorphy of certain Galois
representations to GL_n for n even was established, following work of Harris,
Shepherd-Barron and Taylor and using the lifting theorems of Clozel, Harris and
Taylor. In this paper, we extend those results to n=3 and n=5, and
conditionally to all other odd n. The key additional tools necessary are
results which give the automorphy or potential automorphy of symmetric powers
of elliptic curves, most notably those of Gelbert, Jacquet, Kim, Shahidi and
Harris.
