S.H.
I would recommend not bringing your car seat, and just renting one with the car. A five year old will be more comfortable without it on the plane, I think. We've only taken them on the plane once - the first time we traveled with our daughter. It put her at just the right height to continuously kick the seat in front of her (she was only 15 months old at the time) - we checked it on the way back and have not taken one on since. They really get in the way on the flight in my opinion.