You roll new damage each time the effect is triggered
When a creature enters the spell’s area for the first time on a turn or starts its turn there, that creature must make a Constitution saving throw. The
creature takes 5d8 poison damage on a failed save, or half as much damage on a successful one. (SRD. 125)
There are two ways the effect can be triggered, either a creature:
- starts it's turn within the area of effect, or
- enters the area of effect at any point during it's turn.
And, when a creature does trigger the effect, they immediately:
- make a saving throw, before
- taking 5d8 poison damage (or half on a succesful save).
The amount of damage is decided after the saving throw has been made by the creature and not before. So, it relates specifically to the creature that has triggered it, and made the saving throw, not any other creatures.
This is in direct contrast to 'Instantaneous' effect spells, which are not triggered by the target and deal damage once to multiple targets simultaeneously (ie. Burning Hands).
For evidence of this ruling, that you may consider authoratative, see this Crawford tweet on applying damage from other concentration spells which deal damage repeatedly.
But if you find this too labour intensive, with your DM's permission you could choose to take the average instead, or roll once and keep applying the same figure.
Beware, if rolling and keeping that figure, that the damage will be more extreme. A bad roll would nerf the spell for its whole duration, while a good roll that was applied consistently could seem overpowered. This could result in more metagaming - either from players knowing how much damage they'll take from a DMs spell in advance, or players deciding to drop concentration early, if they rolled poorly on damage, for their own spell.
A comprimise option, to save labour in crowded encounters, that avoids some of these issues, might be to roll damage once per round and apply that figure as necessary.