Split/Second

This is a time-consuming achievement, as there are no huge jumps in the game. The largest ones will only give you a full second, plus a few tenths each time.

The easiest way to accumulate air time is to start up a Quick Race on Downtown Central. When the race starts, you will notice two things - the Space Needle is right there at the beginning of the lap and the race is only two laps, so you can only trigger the Level 2 Power Play at the start of the second lap.

Just hang out at the back of the pack at the start and boost your Power Play bar using Draft. Once it is completely full, use ONLY Level 1 Power Plays for the first lap but MAKE SURE you are back to full before you get to the Start/Finish line, as that is where the Level 2 Power Play for the Space Needle is triggered.

Once the Route Change is triggered, the Needle will fall, allowing you to take out several Rivals at the same time. Also, this gives you the path through it that will give you FOUR jumps of at least one second each. Remember to take the right-hand ramp once your clear the Needle (it's the ramp under the billboard) From here, just finish the race as normal, using Level 1 or 2 Power Plays to take out racers. It doesn't matter whether you win or lose.

The achievement will unlock once the race is over that puts you over the five minutes.

This method allows you to get approximately 5 seconds of Air Time, one Route Change, 7 miles of distance, and between 8-15 Rivals Wrecked per race. You can look at the statistics under the Extras menu, or check at the end of each race.

UPDATE: As noted by Confused Shelf, you can also try the following tracks that will allow you to accumulate time more quickly. As I no longer have the game, I cannot be more descriptive on details on any of these:

Power Plant gets you 6 seconds a race.
Dry Docks gets you 7 seconds a race.
Storm Drain gets you 7 seconds a race.
Canyon gets you 8 seconds a race.
Ferry Wharf gets you 10 seconds a race!
And Storm Drain and Ferry Wharf both take less time than Downtown Central.

This achievement can be obtained more easily if you take advantage of the respawn provided on a certain map. Choose Ferry Wharf and change the route to destroy the aircraft carrier, just before doing the first jump in the ramp we deviate towards the road at the right and you will be automatically destroyed, respawning again in the ramp. Do this as long as you need to obtain the achievement.
Once the race has finished we can check the time we have spent on the air if we press X.