It's my understanding that 9641001 is the first 1970 444 but recent offerings in the Classifieds section has clouded that slightly.
However, with 5736 numbers separating that PIN from your PIN, I think that it's safe to say you own a 1969 444 PK model. That would be the first year of the 444's and the only year for the Performance King designation. If we saw photos of your tractor, then it would help. A clear shot of the seat pedestal and a clear shot of the side of the hood so we can see the hood decal.