Low dimensional free and linear representations of Out(F_3)

We study homomorphisms from Out(F_3) to Out(F_5), and GL(m,K) for m < 7, where K is a field of characteristic other than 2 or 3. We conclude that all K-linear representations of dimension at most 6 of Out(F_3) factor through GL(3,Z), and that all homomorphisms from Out(F_3) to Out(F_5) have finite image.