Hi! I can't seem to figure this problem out, I know the answer, I just can't get it. Could anyone provide me with a solution, or at least put me on the right track to get it? Thanks!

In triangle ABC, AB = 5, BC = 7, AC = 9, and D is on AC with BD = 5. Find the ratio of AD : DC.

The answer is 19 : 8.

Thank you very much for any help!