I am looking for a easy way for dividing a regular hexagon into 5 equal parts and preferably equal shapes or continuing shapes to make it easy to see the regions.
The way that I found is dividing each triangle in the hexagon in five parts (Splitting equilateral triangle into 5 equal parts). But it is difficult to see the 5 final regions.
Best Answer
In the linked page the restriction "obtainable from each other by a rigid motion" makes the question exceedingly hard. You do not need that restriction and the answer becomes very easy without it.
Simply divide the hexagons perimeter into 5 equal parts and connect to the center point.
For example if each side is 1 inch, start at a vertex go to the next vertex of one inch and go 1/5 of an inch into the next side. This forms a triangle of base 1 inch and height $\sqrt{3}/2$ and a second triangle of base 1/5 and height $\sqrt{3}/2$ so the area of this piece is $1.2*\sqrt{3}/4$: 1/5 of the area of the hexigon.
For the second piece go along the side 4/5 of an inch and along the next side 2/5 of an inch. This forms a piece the shape of two triangles glued together. Both have the same height $\sqrt{3}/2$ and the sum of their two bases is $1.2$. So it has the same area as the first piece.
Keep going.
This will work for all regular polygons of course. It will work for all polygons but that might not be immediately obvious.