The concepts of the Fifth and Sixth Dimensions from DC Comics have been on my mind a lot lately, namely due to my interest in the current Justice League story arc, but also due to the fact that the naming of said dimensions may lead to misinterpretations of how their names could lead to people scaling the setting both during and after the current Justice League arc. We know that the Fifth Dimension is meant to hold the place of the actual fifth dimension in DC Comics, but the Multiverse Map also strongly indicates the DC Multiverse functions on String Theory, of which there are 10 dimensions, and DC specifically functions on the Brane cosmological model of String Theory:
We know the drill for the first four, so let's look at the 5th - 10th dimensions as described by String Theory.
Cut out all the pseudo-science mumbo jumbo. I hope these two links are more accurate:
https://www.thoughtco.com/brane-2699125
https://www.thoughtco.com/why-are-there-multiple-universes-2698857
According to this, for a 3-D brane Universe like our own, the higher dimensional bulk it resides in is 9-D space. Which greatly simplifies things for me compared to that hocus pocus I got tricked by earlier since, applying that to the Map which directly calls Bleedspace the "Bulk", Bleed-Space is 9-D space. This would comfortably put the Archetypal Realms of the Sphere of the Gods and the Monitor Sphere above 10-D space. Simplifying this idea is that the Wiki already has a number of characters who reside in the Sphere of the Gods who are given tiering that put them above 11-dimensional space.
Now, DC Cosmology's ground-work:
Due to "Convergence", there are now at least five Multiverses floating around inside the Bleed in their own local groups - "evolved" Pre-Crisis, the Post-Crisis 52 Multiverse, the New 52 Multiverse (Pandora merging Wildstorm and Vertigo with DC + Manhattan's manipulations), Original Pre-Crisis, and the "Multiverse" that exists via Hypertime. It is also possible that the original Wildstorm Multiverse also exists within the Bleed.
Moreover, there are individual universes within the Orrery of Worlds with different physics from the rest e.g. Earth 26's Cartoon Physics, Ultraman being empowered by Kryptonite rather than weakened.
While the Multiverse has been reshaped time and time again by various Crises, the Sphere of the Gods remained untouched by those changes, as we know the New Gods retain all memories of all iterations of the Multiverse. So, whatever dimensional space the Sphere of the Gods resides in is far enough above the Orrery of Worlds that changes to the Multiverse there don't affect beings like Darkseid.
The Fifth Dimension of "Imagination" is the energy that flows through the entire structure of the DC Multiverse, from the Orrery to the Monitor Sphere, and exists "beyond time". Yet it is nowhere to be seen on the DC Multiverse Map. In fact, in the recent Justice League arc, Mxyzptlk took the entire Multiverse Map and referred to it as comprising "four dimensions" (from his perspective), including all the branes and bulks observed on it, all the way up to the Monitor Sphere.
Then there is what Mxyzptlk says to Jon Kent here, but that's a lot to unpack right now given it implies the DCAU Multiverse also exists in the Multi-Multiverse within the Bleed. With the recent Justice League arc, we now know the Sixth Dimension is above the Fifth, described by Mxyzptlk as "Beyond imagination", a "realm of the impossible" where the Multiverse was created and set in motion. The only beings able to access the Sixth Dimension previously were the Monitor, Anti-Monitor, World Forger, and Perpetua.
Beyond all of that is the greater Omniverse, containing an infinite number of other Multiverses created by other "Super-Celestials". In Justice League #22, The Monitor demonstrated the ability to observe Multiverses outside the one he was tasked with monitoring (the DC Multiverse).