No, it's not illegal. However, it would be extremely stupid for a 20 year old male to "date" a 15 year old girl. That's because she could tell everyone that they had sex, even though they didn't, and all of the sudden the 20 year old male's reputation is destroyed. In addition, if I were the 15 year old girl's dad, I would wonder just exactly what the 20 year old male's interest in my 15 year old daughter (who is going to turn 16 in six months) could possibly be? They're not in the same peer group, he's old enough to be almost done with college, and she's just barely in high school and cannot even buy cigarettes or vote.
Want my advice? If a 15 year old girl wrote the question, I'd tell her to stick to boys her age. If a nearly 21 year old male wrote the question, I'd tell him he's asking for it and to stick to girls who can rent a movie without being on their parent's account.
Although it is not illegal for a 15 year old to have a non sexual friendship with a 20 year old guy, it is not advisible. If your parents objected to the dating relationship that you descibed, and you defied your parents, they could seek the assistance of the juvenile court for incorrigibility. Do yourself, and your parents a favor, and spend your time with people your own age.