By "enemies" the game actually implies players, which is entirely doable, especially as a strong attacker with tolerable defense/evade stats, for instance Store Manager or the un-nerfed Tomomo in single-player. Getting 5 kills in one match as either is nothing, but surviving in the interim can be tough. In light of this, it's advisable to play on a map with the field effect Regeneration, by default Planet Earth or Sealed Archive, and quite a few heal and defense cards.
This is also very accomplishable on Kai's first scenario featuring Marie Poppo and two enemy-character players, especially on Casual difficulty. Just madly attack everyone you can, and you'll hit 5 before you know it, without too much fear of counterattack as Casual CPU rolls are rigged to be lower and two of the players already have attack debuffs.