Go to https://www.airbnb.com/help and click "Send or Request Money" at the bottom of the page. You will be prompted for a number of things like which guest this request pertains to and how much you want to charge them. You can also put details in a comment field. Keep it brief and succinct, like "Guest paid for 4 guests for 5 nights, but 7 guests stayed. I am charging an extra XX Euro for the extra 3 guests for 5 nights. I saw these guests as they were leaving, and the paying guest confirmed that they stayed there." Don't get into long-winded explanations about luggage, FINA, etc. Let Airbnb sort all that out. Just state the bald facts about why you're requesting more money.
A request will be sent to the guest, which they can't simply ignore. Airbnb will back you up on this and will participate in the action to some degree. I'm not sure how far they can go (for example, I don't know if they can charge the guest's credit card without their permission) but at the very least, the complaint is documented and can be followed up on.
Good luck! And if it doesn't work out, you have the last resort of giving the guest a poor review that includes these details, which will prevent them from being able to book on Airbnb again.