5-7 minutes for a run up in a single seems a bit long. That said if you are worried about other aircraft how about just using your radio and tell the other aircraft you'll be doing a run up at the holding point of wherever. It comes down to common sense and airmanship.
As you fly around the country you'll probably find out that the airports are very quiet compared to the controlled ones you're used to and you'll be the only one moving.
Where you may encounter traffic is if you attend an air show or fly in. Everyone wants to leave at the same time.