The term 'ASK IN EARNEST' can be broken down into two crossword solutions: 'PLEAD' (5 letters) and 'ENTREAT' (7 letters). Both words refer to the act of making a request in a very earnest and sincere manner. Pleading is often used to express strong emotion or urgency, while entreating is more polite and respectful. Both words imply that the person making the request is very serious about it and expects a positive response.