Using first-principles simulations combined with many-body calculations, we show that two-dimensional free-standing quintuple-layer (QL) ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{2}\mathrm{Te}$ is an inversion-symmetric monolayer expected to achieve spatially indirect exciton with large exciton radius, small exciton effective mass, and long exciton lifetime. Such system is theoretically predicted to be a promising platform for realizing excitonic Bose-Einstein condensation and superfluid due to its high phase transition temperatures of $\ensuremath{\sim}257$ and $\ensuremath{\sim}64.25$ K for the excitonic degeneracy and superfluid, respectively. The importance of spin-orbit coupling is revealed, and the angular momentum selection rules for photon absorption are discussed. This finding suggests the potential of QL ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{2}\mathrm{Te}$ monolayer with exotic bosonic bound states provides as a tantalizing high-temperature platform to probe excitonic physics.