  We derive the stability conditions for the M5-brane in topological M-theory
using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is
necessarily non-vanishing, as is the case also for the 2-form field strengths
on coisotropic branes in topological string theory. It is demonstrated that the
self-duality is consistent with the stability conditions, which are solved
locally in terms of a tensor in the representation 6 of SU(3) in G_2. The
double dimensional reduction of the M5-brane is the D4-brane, and its direct
reduction is an NS5-brane. We show that the equation of motion for the 3-form
on the NS5-brane wrapping a Calabi-Yau space is exactly the Kodaira-Spencer
equation, providing support for a string-fivebrane duality in topological
string theory.
