  For $N$-point best-packing configurations $\omega_N$ on a compact metric
space $(A,\rho)$, we obtain estimates for the mesh-separation ratio
$\gamma(\omega_N,A)$, which is the quotient of the covering radius of
$\omega_N$ relative to $A$ and the minimum pairwise distance between points in
$\omega_N$. For best-packing configurations $\omega_N$ that arise as limits of
minimal Riesz $s$-energy configurations as $s\to \infty$, we prove that
$\gamma(\omega_N,A)\le 1$ and this bound can be attained even for the sphere.
In the particular case when N=5 on $S^2$ with $\rho$ the Euclidean metric, we
prove our main result that among the infinitely many 5-point best-packing
configurations there is a unique configuration, namely a square-base pyramid
$\omega_5^*$, that is the limit (as $s\to \infty$) of 5-point $s$-energy
minimizing configurations. Moreover, $\gamma(\omega_5^*,S^2)=1$.
