We observe a nonlinear optical process in a gas of cold atoms that simultaneously displays the largest reported fifth-order nonlinear susceptibility χ (5)=1.9×10 - 12 (m/V) 4 and high transparency. The nonlinearity results from the simultaneous cooling and crystallization of the gas, and gives rise to efficient Bragg scattering in the form of six-wave mixing at low light levels. For large atom-photon coupling strengths, the back-action of the scattered fields influences the light-matter dynamics. We confirm this interpretation by investigating the nonlinearity for different polarization configurations. In addition, we demonstrate excellent agreement between our experimental measurements and a theoretical model with no free parameters, and compare our results to those obtained using alternative approaches. This system may have important applications in many-body physics, quantum information processing, and multidimensional soliton formation. © Europhysics Letters Association 2012.