This achievement is very easy once you know where to go.
1st, settings do not matter...only game type. Go into the "INVASION" game type under match making. Invasion is like RUSH in BadCompany...you have 2 bases and a 3rd objective to take over within the game time. These games are ALWAYS Elites vs. Spartans and they are ALWAYS two rounds meaning you will be Spartans once and Elites once.
5 Kills is not a lot to ask, especially if you are on a map where the Elites are on defense and the Spartans are just running to their deaths. In any case, you will get this in under 5 minutes of playing.
While in Invasion, it is also best to go after this achievement with a friend:
I suggest trying the Invasion Slayer for that one, as the games seem to last longer and there are a lot more kills/deaths.