  We present the light-cone gauge fixed Lagrangian for the M5-brane; it has a
residual `exotic' gauge invariance with the group of 5-volume preserving
diffeomorphisms, SDiff(5), as gauge group. For an M5-brane of topology R2 x M3,
for closed 3-manifold M3, we find an infinite tension limit that yields an
SO(8)-invariant (1+2)-dimensional field theory with `exotic' SDiff(3) gauge
invariance. We show that this field theory is the Carrollian limit of the Nambu
bracket realization of the `BLG' model for multiple M2-branes.
