I may call HR contact and try to make a nice small chat. People caught off guard may sometimes leak some useful information unconsciously, which probably will help you figuring out if there is room for salary growth, and what is the best way to deliver the idea that an extra $5000 increase will make you a happier employee. Email is sort of too formal for me in this situation. People may reply after deliberation, which sounds more like a diplomatese.
Good luck! :)