An algorithm for constructing general static black hole configuration
for the theory of N = 2, d = 5 supergravity coupled to an arbitrary nu
mber of Abelian vector multiplets is given. The underlying very specia
l geometry structure plays a major role in this construction. From the
viewpoint of M-theory compactified on a Calabi-Yau threefold, these b
lack holes are identified with BPS winding states of the membrane arou
nd two-cycles of the Calabi-Yau threefold, and thus are of importance
in the probing of the phase transitions in the moduli space of M-theor
y compactified on a Calabi-Yau threefold.