You would really have to check the dates of birth for both parties. While the two hypothetical persons can surely "date," sexual intercourse between a fifteen year old and another person 48 months older is considered Rape of a Child 3rd degree.
If by "date" you mean have dinner in a restaurant, watch a movie, or other social activities that do not involve sexual or intimate contact, there is no age limit. If by "date" you mean intimate or sexual contact, Washington state's child rape laws are based on age differences between the partners and the age of the younger partner. At Age 15 for the younger partner, there is a 48 month limit on age difference for the older partner.
While this may be the law, it is generally not psychologically healthy for 15 year olds to be sexually active, and certainly not to be sexually active with adults. Generally speaking, it is not normal for 19 year olds to be sexually attracted to 15 year olds.