  We study critical points of the BPS mass $Z$, the BPS string tension $Z_m$,
the black hole potential $V$ and the gauged central charge potential $P$ for
M-theory compactified on Calabi-Yau three-folds. We first show that the
stabilization equations for $Z$ (determining the black hole entropy) take an
extremely simple form in five dimensions as opposed to four dimensions. The
stabilization equations for $Z_m$ are also very simple and determine the size
of the infinite $adS_3$-throat of the string. The black hole potential in
general exhibits two classes of critical points: supersymmetric critical points
which coincide with those of the central charge and non-supersymmetric critical
points. We then generalize the discussion to the entire extended K\"ahler cone
encompassing topologically different but birationally equivalent Calabi-Yau
three-folds that are connected via flop transitions. We examine behavior of the
four potentials to probe the nature of these phase transitions. We find that
$V$ and $P$ are continuous but not smooth across the flop transition, while $Z$
and its first two derivatives, as well as $Z_m$ and its first derivative, are
continuous. This in turn implies that supersymmetric stabilization of $Z$ and
$Z_m$ for a given configuration takes place in at most one point throughout the
entire extended K\"ahler cone. The corresponding black holes (or string states)
interpolate between different Calabi-Yau three-folds. At the boundaries of the
extended K\"ahler cone we observe that electric states become massless and/or
magnetic strings become tensionless.
