  We derive the U-duality charge orbits, as well as the related moduli spaces,
of "large" and "small" extremal black holes in non-maximal ungauged
Maxwell-Einstein supergravities with symmetric scalar manifolds in d=5
space-time dimensions. The stabilizer groups of the various classes of orbits
are obtained by determining and solving suitable U-invariant sets of
constraints, both in "bare" and "dressed" charges bases, with various methods.
After a general treatment of attractors in real special geometry (also
considering non-symmetric cases), the N=2 "magic" theories, as well as the N=2
Jordan symmetric sequence, are analyzed in detail. Finally, the half-maximal
(N=4) matter-coupled supergravity is also studied in this context.
