There are 5 PCs in my group. If a swarm of snakes attacks them does the swarm attack them all 1x per round? 

description of the attack available to the swarm is pretty clear, I bolded it for added clarity:

Bite. Melee Weapon Attack: +6 to hit, reach 0 ft., one creature in the swarm's space. Hit: 7 (2d6) piercing damage, or 3 (1d6) piercing damage if the swarm has half of its hit points or fewer. The target must make a DC 10 Constitution saving throw, taking 14 (4d6) poison damage on a failed save, or half as much damage on a successful one.

It's pretty clear that the swarm as stat blocked occupies a 5x5 "space" and needs to be in the same space as a character to attack it.  Now if you have the PC in a room and every space they're in is covered with snakes, mechanically you're talking about multiple swarms, on for each "square" if you're sticking with traditional mapping/space management.  "Theater of the mind" I'd still figure out the rough space and how many swarms I can fit into it.

Thanks Midnight. That helps me. 

One swarm of poisonous snakes is size medium and takes a 5x5 space. It can make one attack against a creature if it is sharing a space with it.