In one timeline, it's primary species were the Zahl. In another, it was dominated by the Krenim Imperium. The latter originated the Krenim weapon ship which manipulated the timeline of the region extensively.
Given that the grid covered a substantial portion of space (the Krenim Imperium at one point spanned 5000 parsecs yet remained within the grid), the other civilisations Voyager encountered or interacted with, like the Garenor, Mawasi and Nihydron, as well as the Imperium's original rivals the Rilnar, and the other civilizations targeted by Annorax in order to restore the imperium, such as the Malkoth, Ram Izad, likely also were native to the grid.
Grid 005, primary species, Zahl
Grid 005, with the Zahl erased and the Krenim Imperium restored to 98% of its former state
Grid 005, after erasing the Garenor reduces the Imperium to a pre-warp state