There are two cliffs. They are each attached by a suspension bridge that takes 5 minutes to walk across, and is the only way to get to the other side. No one is allowed to cross the bridge unless authorized. There is a guard on the other side that takes a nap every 5 minutes, then keeps watch for 5 minutes, takes a nap for 5 minutes, and so on. Let's say you don't have authorization. How would you get across (Remember, he wakes up EXACTLY after 5 minutes, meaning if you go on the bridge the second he takes a nap, and you cross the bridge, he'll wake up exactly when you reach the other side, and send you back)?
You can't go as he is awake, he'll see you, but go when he doesn't see you. Then, turn back as he is waking up, pretending to go to the side you came from. Then, he'll figure you are unauthorized to set foot on the bridge, and send you to the side you want to get to.