Five-wave Bragg solitary waves in the form of weakly coupled states, occurring within a four-order non-collinear scattering of light by acoustic waves in an optically anisotropic crystal, are identified and investigated. Generally, we study this phenomenon in an arbitrary regime with the phase, i.e. frequency-angular, mismatches, while, for simplicity’s sake, the exact conditions appearing of localization for multi-pulse coupled states is illustrated in a regime of the phase synchronism. The spatial-frequency distributions of the optical components inherent in these solitary waves are investigated theoretically, simulated numerically and observed experimentally in a tellurium dioxide crystal. Much attention is given to the analysis of contributions conditioned by the effect of optical activity in a tellurium dioxide crystal of chosen orientation. The performed analysis makes it possible to estimate the effective photo-elastic constants for both normal and anomalous processes of light scattering rather accurately and, in so doing, to match theoretical estimations for the efficiency of multi-order acousto-optical interaction with the experimental results obtained.