The pentagon $A_1A_2A_3A_4A_5$ contains bisectors $\ell_1$, $\ell_2$, $...$, $\ell_5$ of angles $\angle A_1$, $\angle A_2$, $...$ , $\angle A_5$ respectively. Bisectors $\ell_1$ and $\ell_2$ intersect at point $B_1$, $\ell_2$ and $\ell_3$ - at point $B_2$, etc., $\ell_5$ and $\ell_1$ intersect at point $B_5$. Can the pentagon $B_1B_2B_3B_4B_5$ be convex?