Cyberspace being 5-D:
1. Because of how it pulls dreams and memories out of the headspace of those who enter, and Eggman entered Cyberspace post-Test Run in chronology, it likely pulled his dreams of a fourth dimensional space out of his head and incorporated them into Cyberspace. Cyberspace has statements that indicate universal/infinite size and a temporal component, hence 5-D.
2. Cyberspace was created with the Chaos Emeralds by the Ancients, which under the instruction of the same beings also created Titans with power accepted to scale to 5-D.
3. Eggman acknowledges Cyberspace as more complex and expansive than any digital creation he has constructed at the time, which includes the 4-D space test run maze. See before as to why that would make Cyberspace jump to 5-D.
And for Light Man, his dimensions are classed as “super other-dimensional infinite spaces”, which under the same context as Solaris and the fact Eggman has also constructed 4-D spaces with much weaker technology that has a similar purpose of trapping characters within an alternate space, I think that could be enough to say “super-dimensional” in the context is enough to jump from 4-D to 5-D.