The arguments are put forward that the many pion decays omega ->2 pi^+ 2 pi^-
pi^0 and pi^+ pi^- 3 pi^0 provide an ideal test site for testing the
predictions of chiral models of the vector meson decays into many pions. Using
the approach based on the Weinberg Lagrangian or, in a new language, the
Lagrangian of hidden local symmetry added with the term induced by the
anomalous Lagrangian of Wess and Zumino, the partial widths of these decays are
evaluated, and their excitation curves in e^+e^- annihilation are obtained. The
discussed are the perspectives of the experimental study of the decays omega ->
5 pi in e^+e^- annihilation and photoproduction.Comment: revtex, 12 pages include 2 ps figures; clarifying remarks and
references added, 17-fold reduction of filesize of fig1.ps. Accepted in Phys.
Lett.