I think, the 4K-E motor came in some KE70 corollas, and KP61 Starlets. But these never came to australia so are very rare. (Same with the 3T-E motor).
5K was in the LiteAce van. But these are getting hard to find and the wreckers want good money for one because they know everyone wants one to bolt in a old corolla.
The 5K looks identical to a 3K or 4K, and everything bolts up the same as far as I know.
I think people work 4K's sometimes just because they are cheap, and a 5K is hard to find or costs more. Ask Stewart.
You can usualy get away from having to have a engineers cetificate if you use a 5K. Most states allow you to have a 1600cc in a KE30 without major mods.