Enhancement of supersymmetry near a 5D black hole horizon

Geometric Killing spinors which exist on AdS${}_{p+2\mathrm{}}\times S^{d-p-2}$ sometimes may be identified with supersymmetric Killing spinors. This explains the enhancement of unbroken supersymmetry near the $p$-brane horizon in $d$ dimensions. The corresponding $p$-brane interpolates between two maximally supersymmetric vacua, at infinity and at the horizon. A new case is studied here: $p=0\mathrm{}$, $d=5\mathrm{}$. The details of the supersymmetric version of the very special geometry are presented. We find the area-entropy formula of the supersymmetric 5D black holes via the volume of $S^3$ which depends on charges and the intersection matrix.