Seems like her birth year might be 1965. She says
in this performance, that she was 20 when composing music for Castlevania. Since the game was earliest released on
26 Sep, 1986, and she had already turned 20 by then -- she must've turned 20 by the end of 1985 (assuming she worked on Castlevania between 31 Dec 1985 and 26 Sep, 1986), which would mean that her year of birth is 1965.
Edit: Also, here's another reference:
http://www.giantbomb.com/kinuyo-yamashita/72-39875/