Juice them out. They have to fix your car, when I was rear ended, I got 2000 over the price of what the company said just because I decided to have the body shop juice them. The parts needed are REQUIRED to drive the car on the street and being as your car is fairly new, just ask them for a fat check and go crazy on the used section of this forum
but technically, you don't need new headlights so it might go either way with that one. You definitely need a new radiator support and if the company doesn't wanna budge, you can always write a note to the corporates there. Gieco is a major insurance brand and they have to honor what the body shop says but being as 1400 is extra, they might not. But it is your right to have OEM parts on your car. You can go replica but its up to you. Save a few bucks or get quality over quantity ? Btw, you're lucky
I would love for someone to back into my car that hard lol! Id juice the shit out of them and being as your transmission was in park or if you are 6mt, you can also comp out for money on the trans and/or ebrake system
always loop holes, just gotta search for it. Either way even if the wheels didn't spin, there was enough torque to push the car back 5 feet. That's major damage IMO and that kinda stress anywhere on the transmission or braking system can be horrible.
In short, id ask for all of the above plus extra money for the transmission or brake system (due to the car being pushed 5 feet back), a new bumper rebar (even if not damaged a lot can still cause a fatal outcome in a crash), and maybe even new sensors for your air bags (of course these are all just to get extra cash.) Id still play safe and get everything 100% checked though even the transmission. That much force can lock your tranny or break a synchro or something. If it was 5 inches, hey fine you can pass, but 5 feet... that's a lot of moving that's being stressed on your car.. good luck with your car!