It's only 4D. I believe they called it 5D chess because they didn't want people to interpret this as 3D chess + time. If I recall correctly, the tutorial mentions at some point that the 5th dimension is "unused".
5. The timeline of how the game actually evolves, building out the tree. This is a bit of a stretch, since you can't move pieces through it in the same way as the other four.
It would have been nice if 4D only ever meant four spatial dimensions, and then we'd have (3+1)D for three spatial dimensions and a time dimension. (And (2+2)D for two spatial and two time dimensions :-))
