“5” is such an arbitrary number.
Culturally? New York and California dominate, California or New Jersey (they’re almost clones of each other, except guidos v. porn) are #2s for diversity and probably openness, probably in no particular order after more northeastern postage stamp and less northwestern coastal states in general. You might throw Illinois somewhere in that last bunch, but it doesn’t fit geographically. Rule of thumb: states with gay marriage, starting with the ones with more international makeups. Vermont and Maine are probably near the bottom.
Industrially? ⅔ of the main Axis Powers (hint: not Italy), Korea, China, California, Texas, New York, New Jersey, and in no particular order Massachusetts or Washington. I’m thinking R&D centers, not just places with lots of industry growth because those probably would be more Southern states.
You missed post-industrially. That list might be California, New York, Massachusetts, North Carolina, and then pretty much any other state with a top-tier research school. This is a broad category diffused across the country, but perhaps most importantly California and New York probably dominate media in different ways. It ties back into culture; if you regard information sector economics as “progressive” then it would tip California unambiguously ahead of New Jersey.
You also missed political progressiveness. This is probably dominated by New England states, but after them probably northwestern states. I’m tempted to give Colorado and Washington way more props for scaling back drug war thuggery, but really it was just marijuana. States lead the way on gay marriage arguably deserve the highest marks. Most politically conservative states: New York, California. Nothing changes until it has to.