Insulating an attic ceiling
You cannot achieve R38 in only 5 1/2 inches.  One of the highest rated insulations is spray foam, and it is around R6 per inch, which would require 6 3/8 inches at least. If you did fur out the rafters with 2x2s (1.5 x 1.5) then you would have 7 inches total to use and could install 1/2 inch baffles and have closed cell spray foam installed.  It would be expensive, but would give you a thickness of 6.5 inches, and provide R38.