It’s important to understand that these dimensions are just hypothetical. There’s no evidence that they actually exist. Something called string theory requires these extra dimensions to work, but there’s no evidence that string theory is correct or that these dimensions actually exist. Our universe is demonstrably one of 4 dimensions – 3 of space and one of time. Anything beyond that is speculative.
As for how these dimensions exist, in string theory, they’re “compactified.” It’s hard to eli5 but the best way to understand it is that they exist on scales too small for us to notice or interact with. Maybe this example will help: A human hair to use might as well be 1-dimensional line, right? We can only interact with it in that manner. But now imagine that you’re a tiny mite that lives on your scalp. At that scale, an individual human hair would be much larger, and as a mite, you could interact with it in all 3 dimensions. You could walk up and down it, across it, and around it.
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