M5-brane Effective Action as an On-shell Action in Supergravity
  We show that the covariant effective action for M5-brane is a solution to the Hamilton-Jacobi (H-J) equations of 11-dimensional supergravity. The solution to the H-J equations reproduces the supergravity solution that represents the M2-M5 bound states. 
Matsuo Sato and Asato Tsuchiya