  Using $N = 2$ supergravity formalism, we investigate certain behaviors of
five dimensional black objects from the compactification of M-theory on a
Calabi-Yau three-fold. The manifold has been constructed as the intersection of
two homogeneous polynomials of degrees $ (\omega+2,1)$ and $ (2,1) $ in a
product of two weighted projective spaces given by $
\mathbb{WP}^{4}(\omega,1,1,1,1) \times\mathbb{P}^{1}$. First, we determine the
allowed electric charge regions of the BPS and non BPS black holes obtained by
wrapping M2-branes on appropriate two cycles in such a proposed Calabi-Yau
three-fold. After that, we calculate the entropy of these solutions which takes
a maximal value corresponding to $\omega=1$ defining the ordinary projective
space $\mathbb{P}^{4}$. For generic values of $\omega$, we show that the non
BPS states are unstable. Then, we conduct a similar study of five dimensional
black strings. Concerning the allowed magnetic charge regions of the BPS and
non BPS black stringy solutions derived from M5-branes on dual divisors, we
calculate the tension taking a minimal value for $\mathbb{P}^{4}$. By
determining the recombination factor, we show that the non-BPS black string
states are stable in the allowed regions in the magnetic charge space.
