This is an easy, fool-proof solution even if you have a weak character and/or weak weapon (and absolutely no aim, like myself):
Go to the tunnel on the SW corner of the map.
Inside that tunnel that takes you to Moresby, there's a fire. Some infected will come running at you in flames.
If you got there in a vehicle, just park it inside the tunnel (not too far inside or you will travel to Moresby).
This is the easy part. You DON'T have to do the killing blow. Just kick the zombie once (and once only) and jump on top of you car and let it die. If you got there on foot, just avoid the zombie (after kicking him once) until it dies.
Rinse and repeat four more times.
I call it the "Hit-and-run-like-a-girl" solution.
NOTE: If you run out of zombies just reload your last checkpoint and go to the tunnel to get your missing zombie(s) avoiding confrontation with other zombies on the way.
NOTE 2: As noted by grasn reloaded, it seems that the higher the level, the longer it would take the fire to kill the zombie. So try this solution early in the game if possible.