When informing your professor of a situation, it's very important to be specific. If your reasons are "stress" or "an emergency," chances are your professor won't give you the extension. Asking for an extension is already an inconvenience, and if you're not specific you will likely not get a response, just a failing grade. However, if you fully explain the situation and its specifics, you will increase your chances on that extension. The truth will set you free from that looming deadline.