  BPS and non-BPS orbits for extremal black-holes in N=2 Maxwell-Einstein
supergravity theories (MESGT) in five dimensions were classified long ago by
the present authors for the case of symmetric scalar manifolds. Motivated by
these results and some recent work on non-supersymmetric attractors we show
that attractor equations in N=2 MESGTs in d=5 do indeed possess the distinct
families of solutions with finite Bekenstein-Hawking entropy. The new non-BPS
solutions have non-vanishing central charge and matter charge which is
invariant under the maximal compact subgroup of the stabilizer of the non-BPS
orbit. Our analysis covers all symmetric space theories G/H such that G is a
symmetry of the action. These theories are in one-to-one correspondence with
(Euclidean) Jordan algebras of degree three. In the particular case of N=2
MESGT with scalar manifold SU*(6)/USp(6) a duality of the two solutions with
regard to N=2 and N=6 supergravity is also considered.
