The evaluation of the branching ratios of the decays $\phi(1020)\to2\pi^+2\pi^-\pi^0$, $\pi^+\pi^-3\pi^0$

Combining the Okubo–Zweig–Iizuka rule in the decay $\phi\to\rho\pi\to\pi^+\pi^-\pi^0$ with the $\rho\to4\pi$ decay amplitudes, we calculate the $\phi\to2\pi^+2\pi^-\pi^0$ and $\phi\to\pi^+\pi^-3\pi^0$ ones. The partial widths of the above $\phi$ decays are evaluated, and the excitation curves in $e^+e^-$ annihilation are obtained, assuming reasonable particular relations among the parameters characterizing the anomalous terms of the HLS Lagrangian. The evaluated branching ratios $B_{\phi\to\pi^+\pi^-3\pi^0}\approx2\cdot 10^{-7}$ and $B_{\phi\to2\pi^+2\pi^-\pi^0}\approx7\cdot 10^{-7}$ are such that with the luminosity $L=500 pb^{-1}$ attained at DA$\Phi$NE $\phi$ factory, one may already possess about $1685$ events of the decays $\phi\to5\pi$.