5D space is from the Marathon games.
Marathon’s levels are 2D, but are rendered in 3D.
5D space is a side effect of having 3D movement in a 2D map.
There are portals that clip polygons from view.
Areas can overlap, but they don’t intersect.
All this is done with portal rendering.
Not like the Portal games, instead more like Doom 3.
If you mix Doom 3 portal rendering with Marathon portals, you get 5D space in full 3D.
I’m working on mixing Doom 3 and Marathon to make something new.
What?
3D+2D makes 5D. Simple mathematics! 
That’s how i get things done for sure.
Looking at what little you find online for “marathon 5D” it refers to a tardis-like effect where going through a passage makes the world look way different compared to what you’d see when coming to the very same spot through a different passage.
It can be an interesting game mechanic (albeit not something brand new). Sounds interesting that they somehow achieved that with 2D rendering? Not sure. It explains the old doom-like graphics.
From a gameplay perspective: Combine that with some time-warp ability/feature (where you can temporarily see things from the past, or influence something in the past to change the present) and you have a truly brain melting 5D (puzzle) game