The mutant attack in the terminal in the "Gaining Influence" mission presents the perfect opportunity to unlock this achievement. Simply deploy a Sentry Turret and let it take out at least 5 enemies on its own. If the Sentry Turret is knocked down or destroyed before killing 5 mutants, you must deploy another one, at which point the count starts over. Stand guard and prevent the Sentry Turret from getting knocked down to reach the goal. Another good place to get this is during the Mutant Bash TV show (thanks to fastNcurious for this info).
I got both the sentry gun and spider bot achievements in the sewer in about 2 minutes. They just swarm you. Start on the top level and place the sentry. After you get that one reclaim it parts and put down the spider bot and start walking down the stairs and up the stairs you see mutants come down. Takes very little time. This was the sewr between the Ark and the Hagar settlement.
I had trouble getting this achievement with the standard turret. The mutants kept on attacking the turret and breaking it before it had killed 5 of em. I managed to get the achievement after I had upgraded to an advanced turret though, they're much sturdier so harder for enemies to break em.