'Appropriate' levels are simply that a child should be making progress each year. How that child fits in relative to everyone else, isn't necessarily relevant.
We have students in yr8 with end of yr targets ranging from 3 to 8, depending on their ability.
Note also that different subjects have different level systems, so where a '5' might be average in some subjects, it might be above average in others. (Languages for example, which for most students is a completely new subject, tend to have lower levels in the first couple of years. This applies to some other subjects too.)
Each level has 3 sublevels, so you go:
3c -> 3b -> 3a -> 4c -> 4b -> 4a -> 5c -> 5b -> 5a
In broad brushstrokes, generally we expect students to make 2 sub-levels of progress each year, especially the middle/higher sets. Some of the low ability groups have targets of just 1 sub level each year. Some of the top set students may be set steeper targets.
What sort of special school is it? If he got L5 in English from primary at the end of yr6, I would be expecting him to get L6 by the end of yr8 at least.
What has the school said about the progress he is making?