High resolution Brillouin spectroscopy has been used to study the elastic properties (CH3NH3)(5)Bi2Br11 (MAPBB) crystal in the vicinity of its ferroelectric phase transition at T-C = 311.5 K. Temperature dependencies of eleven Brillouin modes have been observed for the phonons propagating along six different directions: [100], [010], [001], [110], [101] and [011]. The results provided the opportunity to calculate, for the first time, the temperature dependence of all the elastic constants above and below the mmmFmm2 phase transition. Different types of coupling between the order parameter (spontaneous polarization P-S) and the elastic degree of freedom have been observed and discussed.