This method will not only unlock spending 5 minutes in the air but also riding a lawn mower for an hour and wrecking and getting wrecked 100 times achievements. It will also give you a good amount of xp that will go towards the rank achievements.
TRACK: Madman Stadium, Demolition Area
CAR: Lawn Mower
EVENT: Deathmatch, 23 opponents, 20 mins, damage normal
DIFFICULTY: Only change AI difficulty to Expert, leave everything else the same.
What you want to do is keep on going back and forth on the ramps and drive off the edge of the ramps. This will eventually lead to having 5 mins in the air and will also help you getting wrecked 100 times. While going towards the edge of the ramps you can try to wreck some Ais. Though on expert I had no problem getting kills. You will do this 3 times and by the end you should have all four achievements.