All his GK skills are good, plus a few key others, but it seems daft if he stops at 5, when his Limit is 6.........
Look at his last match, what was his improvement bonus? Were it 0.03 or were it normal?
You won't get CA6 from a keeper training him, he will stop, and the only way he will keep improving is playing matches, look carefully his match bonus, if his CA is 5, and his LA is 6, his match bonus should be normal, not the minimum match bonus that a player CA=LA or CA>LA receives.
Also consider that GK skills:
Until 13: they improve normally (match bonus should be 0.40, if PR is 5)
Between 13 and 17: they improve 1,5 times slower (match bonus should be around 0.24, if PR is 5)
Between 17 and 20: they improve 3 times slower (match bonus should be around 0.13, if PR is 5)
If you've got a LA8 outfiel player, you'll have the same issue when he reaches CA7.