Hopefully a jeweler will reply. They may say it can be done, but you'll end up with an oval shaped ring. I don't consider rings that are more or less than one full size different from my ring size.
It can only be done by building a sleeve to fit inside the existing ring, To try to do it any other way will end up with a horrid egg shaped thing, and the top will still be too large for your finger.
If you build a sleeve they can also address that horrible hollow top which is going to be hard on your finger to wear as only the two narrow rails will be supporting the weight as it is which will leave rails indented into your finger.
Even if you build a sleeve however, I fear that the top of the ring, built for a size 9.5 is going to be massive on top of a size 5.5 finger.