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How is solving a rubik's cube ANYTHING like self driving?

It isn't. Solving Rubiks Cube is trivial. Anybody can learn to do it, and many people can solve a randomized cube in under a minute.

A computer can find the solution in a few microseconds. The hard part isn't finding the solution in software, but building a mechanical contraption to rapidly twist the cube without breaking it. This is an achievement in mechanical engineering, not software. TFA completely skipped over the substance to focus on the trivial.

You do not RC. The real Rubik's cube has always used stickers. Only recently have Rubik's started manufacturing cubes with coloured plastic sides.

Sorry, but you don't actually have a unique rarity on your hands. 5x5x5 Rubik's Cube's can be bought for about $30 in any good toy store. If you like ordering online, they're available direct from the manufacturer along with all the other versions. Also, that simulator you requested has already been written. There is a general Rubik's cube simulator available here which can simulate a cube of any size.

As to being too difficult to solve, the world record for solving one of these is 1:47.22 (that's less than two minutes). You can check out lots of records on this speedcubing site. The 4x4x4 is really pretty similar to the 3x3x3, except with extra algorithms needed for the new peices that are present. If you can solve a 3x3x3, you're most of the way to the 4x4x4. The 5x5x5 is a similar extension of the 4x4x4.

For the record, I can solve the 4x4x4, but my times are pretty awful. I don't have good algorithms for solving those extra peices, and I don't do it often enough. On the 3x3x3, though, I can consistently do it in 1:30, and that's just with home-grown algorithms some friends and I came up with.

I think you've been had. I have a 5x5 that I bought at the local game store, and there were more than 5 there on the shelf. It's called a Rubik's Professor. It's actually not that tricky to solve, just time-consuming. I can do a 3x3 in a couple of minutes, a 4x4 in half an hour, and a 5x5 in a couple of hours.

Nowhere do they mention the last dimension of the cubes

Yup - go to Rubiks site and buy a 2x2x2, 3x3x3, 4x4x4 or even (The Professor) 5x5x5 (although they refer to them as nxn too!)

Seven Towns still makes Rubik's toys, though the current color scheme for the Magic puzzle isn't the same as the cooler original that Matchbox made. However, they now sell do-it-yourself kits that allow you to make your own Magic puzzles.

The trademark infringement complaint, according to the article, ....

Of course, what else would you expect from the likes of an Associated Press reporter?

A little research turns up the fact that not only has Seven Towns Limited trademarked Rubik and Rubik's Cube, they have trademarked its appearance. You might want to check out this, this, and this before continuing your sophistry. Realizing that one might actually have to search a bit on the last referenced page to find the relevant commentary, I'll post it here:

March 2004

Section: 7th Circuit.

Gary Ropski was quoted in the March, 2004 publication of Corporate Legal Times in an article discussing the Seven Towns v. Hazco lawsuit concerning the Rubik's Cube. Mr. Ropski, counsel for Seven Towns, commented on Hazco saying that, "they know how valuable the Rubik's Cube trademark and trade dress are because they tried to get a license from Seven Towns to use it. . . After being refused permission, they used it anyway." He continued by saying, "The U.S. Patent and Trademark Association granted Seven Towns a trademark for the appearance of the Rubik's Cube. It's a violation of federal law to infringe that trademark by making a product that's confusingly similar."

The trademark infringement complaint, according to the article, ....

Of course, what else would you expect from the likes of an Associated Press reporter?

A little research turns up the fact that not only has Seven Towns Limited trademarked Rubik and Rubik's Cube, they have trademarked its appearance. You might want to check out this, this, and this before continuing your sophistry. Realizing that one might actually have to search a bit on the last referenced page to find the relevant commentary, I'll post it here:

March 2004

Section: 7th Circuit.

Gary Ropski was quoted in the March, 2004 publication of Corporate Legal Times in an article discussing the Seven Towns v. Hazco lawsuit concerning the Rubik's Cube. Mr. Ropski, counsel for Seven Towns, commented on Hazco saying that, "they know how valuable the Rubik's Cube trademark and trade dress are because they tried to get a license from Seven Towns to use it. . . After being refused permission, they used it anyway." He continued by saying, "The U.S. Patent and Trademark Association granted Seven Towns a trademark for the appearance of the Rubik's Cube. It's a violation of federal law to infringe that trademark by making a product that's confusingly similar."

for those of us that are now curious but can't afford one!
Java Cube

You mean these ?