Lots of advice. My advice is coming from my experience managing a Body Shop.
For starters, DON'T GO TO GIECO's RECOMMENDED SHOP! That shop is a GEICO approved shop, and the reason they are "Approved" is because they do the repairs cheaper, thus saving the insurance company money. Second, Tesla WILL NOT SELL CERTAIN PARTS TO NON TESLA APPROVED BODY SHOPS! and I cannot stress that enough. Next, the Tesla approved shop will More accurately be able to give a quote for repairs. The GEICO approved shop will be mostly guesstimating based on "normal" cars. If your trunk hatch is damaged, this is going to be a MAJOR REPAIR! Especially being the car is 5 days old.....
PLEASE PLEASE PLEASE DO NOT GO TO THEIR APPROVED SHOP! ONLY, AND I REPEAT, ONLY HAVE A TESLA APPROVED SHOP LOOK AT IT AND GIVE A ESTIMATE! By getting a Low Ball GEICO approved shop estimate, that gives GEICO a load of ammunition to fight you in repair costs down the road. Remember, THIS IS NOT A GEO METRO! THIS IS YOUR BRAND SPANKING NEW TESLA MODEL S, The most technology advanced production car in the world!
Also, MAKE SURE you have a INDEPENDENT AUTO APPRAISER come in and look at the vehicle, before AND after the repair (AND show repair receipts for the total cost of the repairs). Then follow up with GEICO for Diminished Value of the vehicle. You may even want to bring that up from the get go, as if the repair costs are high (The trunk lid is not going to be cheap, that will be a complete replacement, not repair on a 5 day old car), Plus the diminished value, may push the repairs too close to the "Totaled" mark, and you may be getting a new replacement vehicle. I know I would not settle for a repaired vehicle without A LOT of compensation (and I have personally been in this boat with my Nissan).
Just as a example on Diminished value, when my Nissan CUBE was 1 year and 4 days old, wife got rear ended at a stop light. Mind you I paid 15,400 for the car. I got $3k in diminished value, on top of the 6k they payed for repairs. Thats some good money, and that was a 1 year old econobox.
Just repeating again, DO NOT TAKE IT TO THE GEICO SHOP!
Not a Geico recommended shop. I know this for a fact. They are a Tesla approved/recommended shop. My car got backed into, and I took it there on the advice of Tesla. They did a superb job, and the repair is imperceptible. They had to replace the entire rear quarter panel due to a crack in the aluminum. Paint matching was excellent also. They had about 9 Tesla's there when I dropped mine off. They impressed me with their expertise, and they fought Geico to get all the repairs done the right way.