An easy method for doing this requires meat bait and molotovs.
Fast travel to the Arena Lobby and enter Arena A, as it has a great place to do this achievement.
Upon entering the arena you will notice two large, red, and explosive barrels to your right. Once zombies begin spawning, lure a group of them to one of these barrels. Then, throw a meat bait at the barrel. The meat bait will distract the group of zombies and keep them near the barrel. This gives you the perfect opportunity to throw a molotov, hitting both the zombies and the explosive barrel. The molotov will set the zombies on fire, and the barrel will explode soon after, netting you kills and progress towards this achievement.
Do not worry if you don't get all 5 kills in one go. This achievement is cumulative, meaning you could get 3 kills in one attempt and 2 in another, and still unlock it.