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So what is 5nm or 3nm?

The process marketed as 5nm has roughly twice the density as the process marketed as 7nm and so on up and down the line; that's how they justify it.

How can they double the density without decreasing the feature size?

The feature side usually does decrease every generation; it's just that the feature size for, say, a "7nm" process is not exactly 7nm.

The power of recursive reasoning. Induction tells us that Intel's 10nm process probably wasn't 10nm features...

I am wildly speculating here, but maybe going 3rd dimension?

It has about the same meaning as the 5 or 3 in "core i5" or "core i3". It's all marketing.