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We experience 4 dimensions although we can only move through the three physical dimensions for the most part. Each subsequent dimension is an infinitely perpendicular locus of the previous dimension. Take a 0 dimensional point, extend it infinitely perpendicular to itself and it becomes a line. Take a 1d line, infinitely extend it perpendicular to itself and you get a 2d plane.
So a 5d person would have immediate access to two neighboring 4th dimension universes because it is an infinitely extended locus of 4d universes in both directions. That's why at 5d you have access to two dimensions, not just one.
6d would have access to potentially infinite dimensions as it would have a locus of alternate dimensions.
Such a being might think itself a god! Until it realizes with horror that all timelines and universes converge into a single point. And nothing they can do is able to change it. Then maybe they'd start flipping out a little.