As a Potterhead, this Peeves me. The only cores are the heartstrings of a dragon, the feather of a phoenix, and the hair of a unnicorn.
Holly wood is 5/20, or 1/4
Dragon scale is 4/20, or 1/5
Add the two together.
5/20 + 4/20 = 9/20
However, do consider that there is one chance of those 'nine' that it can be both, and since the problem asks for 'or', take that out.
9/20 - 1/20 = 8/20 = 2/5
P(A or B) = 9/20