  By using the recently proposed prescription arXiv:0804.3629 for obtaining the
$M5$ brane action from multiple $M2$ branes action in BLG theory, we examine
such transition when 11 Dimensional background antisymmetric fluxes couple to
the $M2$ brane world volume. Such couplings was suggested in arXiv:0805.3427
where it was used the fact that various fields in BLG theory are valued in a
Lie 3-algebra. We argue that this action and promoting it by Nambu-Poisson
bracket gives the expected coupling of fluxes with $M5$ brane at least at weak
coupling limit. We also study some other aspects of the action for example, the
gauge invariance of the theory.
