It is Geometry, isn't it?

Having 5 points, where no three are collinear we can make a pentagon, tetragon or a triangle. There is only $1$ possibility to make a pentagon, choosing all the available points. To make a tetragon we have to pick 4 points, we can do this in 5 different ways:

$\left( \begin{matrix} 5 \\ 4 \end{matrix} \right) =\frac { 5! }{ 4!(5-4)! } =5$

There are 10 possibilities to make a triangle, picking 3 points:

$\left( \begin{matrix} 5 \\ 3 \end{matrix} \right) =\frac { 5! }{ 3!(5-2)! } =\frac{5!}{3!2!}=\frac{4\cdot 5}{2}=10$

So we can make:

$1+5+10 =16$ polygons