How is she Higher-D? i checked her Profile and the only thing that seems to possibly grant any-form of Higher-Dimensional is this.
"
Incorporeality (Her true form is nothing more than her domain being the space-time itself)"
Which from first-glance doesn't seem to be above 5-D at all. it actually seems to be 4-D since her true form is one with her domain which is Space-Time, Space-Time is inherently 4-D until more context is given if Space-Time within Nasuverse is above 5-D or not.
Sure she could have those passives but i don't know if the effects of the Akashic Records are passive as well, that's why i'm asking you to just create a Versus Thread so more knowledgeable people on the verse can explain it more in-depth then i can since i haven't Vampire Hunter D at all.