  We consider general black holes in D=5, N=2 supergravity coupled to vector
multiplets, and discuss the issue of microstate counting from various
viewpoints. The statistical entropy is computed for the near-extremal case
using the central charge of the $AdS_2$ factor appearing in the near-horizon
geometry. Furthermore, we explicitly construct the duality transformation
connecting electrically charged black holes to magnetically charged black
strings, under which the $AdS_2 \times S^3$ near horizon geometry becomes
$AdS_3 \times S^2$. For $AdS_3$ the counting of microstates correctly
reproduces the Bekenstein-Hawking entropy, thus resolving the discrepancy
previously found for $AdS_2$.
