Tha'ts good news. Let me give you one more site to look at. Its got a bit more info on ADD. I mention that because a child with ADD does look very different than a child with ADHD. The site is - http://helpguide.org/mental/adhd_add_signs_symptoms.htm
By the way this site also has some very good parenting/schooling tips.
You might also want to talk to his teacher again - but focus not on his behavior. Instead focus on how he studies, listens, follows directions. These are all important clues that can help a doctor.
Had a feeling when you said you could not get an assessment till 6. Over here we have finally realized the sooner we can get help for a child, the better the chances for recovery (and cheaper in the long run). Best wishes - let me know how things work out.
Let me know (if you don't mind) how the assessment goes, perhaps based on that I can direct you to more resources. One other question. We have CAMS in California. I know they also have CAMS in England - and probably various other places. It does make a difference as to the resources (and school laws) available. I am guessing that because you were told she couldn't be assessed until she was 6, that you live in England?
She may care a tiny bit more than you know as part of the 'scam' is pretending you don't care. I'd try the chores with her which would be torture for you making her do them------- but effective in making her see that she causes negative outcomes with undesirable behavior. ????? ;Ugh I know it is hard and some kids can be so challenging at times. I'd work to understand her add/adhd a bit more and then go from there. Also reward your son in front of her for letting go or moving on from a fight. Might show her that good gets good, bad gets bad