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It was proved earlier that there are 6 isomorphism classes of hyperplanes in the dual polar space (5,q)$, $ even, which arise from its Grassmann-embedding. In the present paper, we extend these results to the case that $ is odd. Specifically, we determine the orbits of the full automorphism group of (5,q)$, $ odd, on the projective points (or equivalently, the hyperplanes) of the projective space (13,q)$ which affords the universal embedding of (5,q)$

Points and hyperplanes of the universal embedding space of the dual polar space DW(5,q), q odd