We study the stability and the dynamics of many-soliton molecules in dispersion- managed optical fiber with focus on 4- and 5-soliton molecules by analytical and numerical means. We calculate in particular their binding energy, pulse width and their chirp using a variational approach. We found that our variational calculations agreed favorably with the numerical solu- tions of the nonlinear Schrödinger equation and they well describe the intensity profiles of the experimental molecules.