  We show that the global mixed gauge-gravitational anomaly of the worldvolume
theory of the M5-brane vanishes, when the anomaly inflow from the bulk is taken
into account. This result extends to the type IIA and heterotic $E_8 \times
E_8$ five-branes. As a by-product, we provide a definition of the chiral
fermionic fields for generic non-spin M5-brane worldvolume and determine the
coupling between the self-dual field and the M-theory C-field.
