The best way to do this achievement is to aim to complete the challenges found in your Spartan hub (this commonly starts on your loadout's and name etc so flick up on LS). Here you can see your progress towards challenges and offer huge amounts of XP. There are challenges for the campaign/multiplayer and the spartan ops, so mix and match. You will eventually reach this in time so keep going. It shouldn't take long at all, probably for most gamers it will be achieved in the first hour or so and will be achieved through playing 3 or 4 online games.
As SeraphimNeeded has noticed in his experience: 'if you somehow end up passing by rank 5, like I did using bonus XP from Waypoint, then you'll need to earn another level naturally before the achievement unlocks.' Hopefully this will put more people at ease