  Pick $n$ points $Z_0,...,Z_{n-1}$ uniformly and independently at random in a
compact convex set $H$ with non empty interior of the plane, and let $Q^n_H$ be
the probability that the $Z_i$'s are the vertices of a convex polygon. Blaschke
1917 \cite{Bla} proved that $Q^4_T\leq Q^4_H\leq Q^4_D$, where $D$ is a disk
and $T$ a triangle. In the present paper we prove $Q^5_T\leq Q^5_H\leq Q^5_D$.
One of the main ingredients of our approach is a new formula for $Q^n_H$ which
permits to prove that Steiner symmetrization does not decrease $Q^5_H$, and
that shaking does not increases it (this is the method Blaschke used in the
$n=4$ case). We conjecture that the new formula we provide will lead in the
future to the complete proof that $Q^n_T\leq Q^n_H\leq Q^n_D$ , for any $n$.
