Many years ago I designed several cuboids. Most of which I made but one I never got round to was the 2x2x5. I based the design around a 5x5x5 core so it would have been absolutely enormous. Some years later Geert Hellings came up with a clever way of making a 2x2x6 from a Master Cube. I adapted this technique to make a fully functional correctly proportioned 2x2x6 and 4x4x6. For some reason I never thought of using Geert's technique to make a 2x2x5. That is until I saw some discussions on the twistypuzzles forum. On 11th Jan 2008 I started to make a 2x2x5. However after a couple of hours I realised I could actually make a 2x2x7, so I did.
I am not going into details about how I made it but you can pretty much work it out from the photos. There is one trick I will share. It is well known that with 2x2xN cuboids you don't have the same "corner will fall out" problem to solve as you do with a 7x7x7 for example. However you can see in my last photo that I have not extended certain parts far enough into the core to prevent them from falling out. What I have done instead is use ball bearings and springs to hold them in place. If you think about a Skewb for a moment, the moves click nicely into place. To start a move you have to apply just that little bit of extra force to get it going. On my 2x2x7 those parts you would expect to fall out aren't going to slide anywhere without additional force. You may have noticed how similar this sounds to my "clip and slide" description of how my fake 9x9x9 'worked'. It's not as fancy but I guess it's a similar simpler variation. Most of the time (90% approx) it is not possible for the parts to fall out anyway so the ball bearings only have to do their work very briefly.
On this puzzle I have used standard Rubik's Cube style stickers.
So how well does it work? The answer is not great. It does work but the second and sixth rows are often difficult to turn. I think the design is OK and if made accurately it would be fine. I made it with a view to make more but currently it is not good enough to produce for other people.
The puzzle can't change shape since it doesn't obey the cuboid shape changing rule-
"A cuboid is capable of shape changing when ( two or more edge unit lengths are different and odd ) or ( two or more edge unit lengths are different and even ) excluding cuboids with a side of one."
In total I have made twelve fully functional cuboids. They are- 2x2x3 (micro), 2x2x4, 2x2x6, 2x2x7, 2x3x4, 3x3x4 (large), 3x3x4 (medium), 3x3x5, 3x4x4, 4x4x5, 4x4x6, 5x5x6.