I have also read somewhere that level 5 in KS2 does not really equate to level 5 in KS3.
My son was a SATs level 5 in sciences and is now working at level 5, like yours. What he is learning is all new to him.
As KS2 is 4 years, should move on 2 levels. However, as KS3 is only 3 yrs, a low 4 will become a 5, a high 4 a 6, a low 5 may also be a 6 and a high 5 should become a 7. A school with a higher value-added score will move them on more than one with a low value-added (on average).
This is interesting; quite a precise account of how much pupils should progress.