Anyone made this yet? It occurred to me that it's essentially the 3x3 Circle Cube, taken to the extreme; the "circles" being larger than the faces. (And not circular, but yeah.)

Could be asily made by fixing the inner center pieces to the core.

Do you mean corners? Fixing the inner centers would just make it a 3x3 with extra cuts.

Take any mass produced 5x5, keep only the centers, corners and middle edges, glue the whole thing with superglue and voila ! Just reassemble it

Hm, what is the problem with only fixing the inner centers to the core? Would't that do the same thing?

It would, but fixing anything from the centers is usually results in a lot of slack. Just look at any of the crazy 3x3x3/tetrahedron/triangular prism puzzles: the circles have a fair bit of play and you need to overturn a bit to get them aligned. Making it the way Greg suggests would result in a far better puzzle, but gluing just the centers will work fine too.