Probably the easiest place to get this achievement if you don't want to bother playing the entire marine campaign before getting it is in a survival match on C Block. This method also allows you to not worry so much about ammo and holding onto a gun that makes you run so slow.
When you start a survival match on C Block, it starts with you locked in a corridor with a smartgun sitting right in front of you with a large stack of boxes beyond it. Grab the gun and start backing up but continue facing the obstruction. The first wave of drones will mostly come up over that obstruction along the ceiling. When you see several of them but before they actually reach you, hold the LT and they should start dying. Most likely, you won't be able to see 5 of them at one time before they start getting into attack range. This should be fine because usually several more will appear in the exact same place as the first few start dying. Whatever you do, remember not to let off the trigger until you are either out of ammo in the clip (at which point you're pretty much SOL and will need to try again) or 5 have died and you got your achievement. Letting off the trigger at any point resets the counter.