  Structural, electronic and magnetic properties of Ti$_5$O$_9$ have been
studied by \textit{ab initio} methods in low-, intermediate- and
high-temperature phases. We have found the charge and orbital order in all
three phases to be non-stable, and the formation of Ti$^{3+}$-Ti$^{3+}$
bipolaronic states less likely as compared to Ti$_4$O$_7$. Several
quasidegenerate magnetic configurations were calculated to have different width
of the band gap, suggesting that the reordering of the unpaired spins at
Ti$^{3+}$ ions might at least partially be responsible for the changes in
conductivity of this material.
