A “dimension” in classical physics is a space through which you can move.
Like space, we appear to move through time in a way we perceive as having points (or coordinates) to it.
Gravity, however, is a property that emerges when a mass interacts with the combined fabrics of space and time called “spacetime”. It somewhat similar to a bowling ball on a trampoline; smaller balls will roll into the “gravity well” created by the bowling ball on the surface of the trampoline.
Higher dimensions (like the 5th dimension) are aspects of mathematical models that attempt to make modern physics more complete.
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