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We study the processes $e^+e^-\to\pi^+\pi^-\pi^0\pi^0\pi^0\gamma$ and$\pi^+\pi^-\pi^0\pi^0\eta\gamma$ in which an energetic photon is radiated fromthe initial state. The data were collected with the BaBar~ detector at SLAC.About 14\,000 and 4700 events, respectively, are selected from a data samplecorresponding to an integrated luminosity of 469~$fb^{-1}$. The invariant massof the hadronic final state defines the effective $e^+e^-$ center-of-massenergy. From the mass spectra, the first precise measurement of the$e^+e^-\to\pi^+\pi^-\pi^0\pi^0\pi^0$ cross section and the first measurementever of the $e^+e^-\to\pi^+\pi^-\pi^0\pi^0\eta$ cross section are performed.The center-of-mass energies range from threshold to 4.35~GeV. The systematicuncertainty is typically between 10 and 13\%. The contributions from$\omega\pi^0\pi^0$, $\eta\pi^+\pi^-$, and other intermediate states arepresented. We observe the $J/\psi$ and $\psi(2S)$ in most of these final statesand measure the corresponding branching fractions, many of them for the firsttime.

physical review. d/physical review. d.

Study of the reactions $e^+e^-\to\pi^+\pi^-\pi^0\pi^0\pi^0\gamma$ and  $\pi^+\pi^-\pi^0\pi^0\eta\gamma$ at center-of-mass energies from threshold to  4.35 GeV using initial-state radiation