  We construct the nonrelativistic covariant world-volume action for a single
M5 brane of $ D=11 $ supergravity in M-theory. The corresponding non-Lorentzian
(NL) background possesses a codimension three foliation and is identified as
the Membrane Newton-Cartan manifold in the presence of background fluxes that
are suitably expanded in $ 1/c^2 $ expansion. We also expand the associated
world-volume fields in $ 1/c^2 $ expansion. The above procedure eventually
results into a well defined world-volume action that is coupled to Membrane
Newton-Cartan background.
