The house of Santa Claus is an old German drawing game for small children. You have to draw a house in one line.  You must not lift your pencil while drawing. $\color{red}{\text{You must not repeat a line.}}$

A possible solution for drawing such a house is:

The drawings sequence is here: 1->2->4->1->3->4->5->3->2

How can one find out all existing drawing sequences using Mathematica?

UPDATE:

each starting position should be possible and the last line should end at the starting postion.