I'm not sure about the limit age (but there shouldn't be anything with ten years age-gap but I'm not sure either, please check them first) but here are some dramas I like:
Destined to Meet You (fl thinking ml and her sleeping together and fl wants to take responsibility since ml is younger but actually it's part of ml's strategy to get close to fl so fl will choose him as her upcoming marriage partner) - fl wants to take care of ml but somehow I remember ml is better at taking care of her
Falling into You (ml want fl to train him so he try to attract her attention by showing his high jump, ml is whiny and cute. Fl then become ml's coach) - fl takes care ml in everything, like a normal coach
Long Vacation (fl and ml becoming roommate after fl's fiancee-who used to be ml's roommate-left her on the wedding day with all of the money. Lively fl makes gloomy ml becoming happier) - my all time favorite, fl is the caring type
Reply 1988 (fl and ml are the same age and neighbours, along with another 3 boys of the same age, 1 older boy, 1 older girl, 1 younger boy and 1 younger girl) - fl takes care of ml since he's a go genius who practically can't do anything other than go
Why Women Love (fl is ml's boss but ml is company's heir, the company owner wish she could teach him about the company. Fl is useless at anything other than works while ml is great at almost everything but he doesn't like to work) - here fl takes care ml at the company but ml takes care of her foods, he's a great cook