The kills must be either simultaneously, with the same grenade, or consecutively - killing anything else inbetween the five will reset the counter. Note that this achievement/trophy cannot be earned on the Dark Waters level. Shrimp hatchlings , amphibians and the Bog shrimp do not count - only the common shrimp. Also note that only frag grenades count, not incendiaries or Claymores.
It can be most easily earned in Sundown, where there are many respawning shrimps. A good place is after you have left the crashed plane, and the bog shrimp has attacked and left - the area around the plane will spawn many shrimp. Fall in the water a few times (not in the same place, or you will die) to get some to spawn, and let them crowd together. They are slow so easy to avoid. Wait until there are five and blow them up! The grenades have a fairly large blast radius, so it is not too difficult. It can be accomplished on Nightfall as well, though there are less common here. Below is a guide if you are having trouble.