By the time i'd finished all the single player stuff i had to boost time for about an hour before the 5 hour achievement unlocked. Please note as per the achievement decription Time Attack does not count toward your time. Nor menu time, this achievement is only calculated when you're actually competing in any mode but time attack (i've yet to do online stuff so unsure if that counts, can't see why not).
Offline>Custom Race>Banana Bay>Poseimon
Pick Random Juicer or Juicer>5 laps
Then pick Easy and put 10 Vehicles in Race
Now pick any racer and confirm, then when the race begins just sit there. The AI should take about 9 minutes (anywhere between 9m10s and 9mins25s) before the race automatically ends so you need to do this around 7 times for the achievment to pop. Obviously the number of races needed will vary from user to user but it popped for me after 7 races.
Just pick Restart each time the race ends and the achievement pops at the end of the completed race once 5 hours racing time has been completed.
Obviously another option is just to play regularly, depending on the enjoyment you get from this game. I do wish time attack counted toward the time, I don't understand that decision as if you are going for the other achievements you'll spend a good few hours there.