  We obtain the Hamiltonian form of the worldvolume action for the M5-brane in
a general D=11 supergravity background. We use this result to obtain a new
version of the covariant M5-brane Lagrangian in which the tension appears as a
dynamical variable, although this Lagrangian has some unsatisfactory features
which we trace to peculiarities of the null limit. We also show that the
M5-brane action is invariant under all (super)isometries of the background.
