  In Spacetime-Matter theory we assume that the 4D induced matter of the $5D $
Ricci-flat bouncing cosmological solutions contains a perfect fluid as well as
an induced scalar field. Then we show that the conventional 4D quintessence and
phantom models of dark energy could be recovered from the $5D$ cosmological
solutions. By using the phase-plane analysis to study the stability of
evolution of the $5D$ models, we find that the conventional 4D late-time
attractor solution is also recovered. This attractor solution shows that the
scale factors of the phantom dominated universes in both the 4D and $5D$
theories will reach infinity in a finite time and the universes will be ended
at a new kind of spacetime singularity at which everything will be annihilated.
We also find that the repulsive force of the phantom may provide us with a
mechanics to explain the bounce.
