Bottomonium $\Upsilon(5S)$ decays into $BB$ and $BB\pi$

Two- and three-body decays of $\Upsilon (5S)$ into $BB,$ $BB^*,$ $B^*B^*,$ $B_sB_s,$ $B_sB_s^*,$ $B_s^* B_s^*$ and $BB^*\pi, B^*B^*\pi$ are evaluated using the theory, developed earlier for dipion bottomonium transitions. The theory contains only two parameters, vertex masses $M_{br}$ and $M_\omega$, known from dipion spectra and width. Predicted values of $\Gamma_{tot}(5S)$ and six partial widths $\Gamma_k(5S), k=BB,BB^*,\dots$ are in agreement with experiment. The decay widths $\Gamma_{5S}(\pi BB^*)$ and $\Gamma_{5S}(\pi B^*B^*)$ are also calculated and found to be of the order of 10 keV.