If you're reading this and don't have any idea what the title means, look back on our page and give it a try!
.... It's not possible, at least when you're not allowed to draw along the edges. Maybe you guessed that but tried it anyway. But here's why: every edge must be crossed once, so each edge is a point of entry or exit to a shape (like the pentagon in the middle). It doesn't matter where along the edge you cross it, so let's draw them in with red:
Now pay attention to the three pentagons, shaded in green above. They have five points of entry/exit, which means that if you try to cross every edge exactly once, you must either start or finish your line inside a pentagon. But wait - a line has only one start point and one end point! This means that it's impossible to draw a line that crosses every edge exactly once in this diagram.
End of spoiler
Now that's settled once and for all, we can all peacefully sleep again.