Disjoint empty convex pentagons in planar point sets

In this paper we obtain the first non-trivial lower bound on the number of disjoint empty convex pentagons in planar points sets. We show that the number of disjoint empty convex pentagons in any set of n points in the plane, no three on a line, is at least $\left\lfloor {\tfrac{{5n}} {{47}}} \right\rfloor $ . This bound can be further improved to $\tfrac{{3n - 1}} {{28}} $ for infinitely many n.