There seems to be some confusion around this achievement, hopefully I can clear it up!
"5:1 damage-to-kill ratio" means, you need to inflict 5 times the amount of damage to your kills, the best method for this is to just back up other players and cause as much damage as possible.
If you get 1 kill, you need to inflict a score of 5 for damage, if you get 5 kills then you'll need to inflict 25 points of damage.
You can see your kill/damage ratio by looking through the in game leaderboards, you can also see it in the post game leaderboards, which I realise will be too late if you've not got the achievement, but you'll get an idea of what tactics to use and such.
Lastly, you don't need to get exactly 5:1 damage to kill, your damage can be higher then that ratio. For example getting a ratio of 11:1 would still unlock the achievement!