Keep in mind that any and all steps described below could hurt you financially, physically or even morally if done improperly. Always follow the instructions of tool manufacturers and apply the most rigorous logic to situations. When a handheld drill manufacturer says to ensure that whatever you're drilling on is securely attached to something sturdy, don't assume "my friend is holding it" as "securely attached". Use clamps and proper jigs while following all instructions supplied, and treat both blunt and sharp tools with high respect — especially the sharp ones. If you are unsure of a step, seek help from someone more knowledgeable. Ashamed? Just ask him to teach you how to do it.
If you have to enlarge the hole, you need a hole saw. You can usually buy a $20 or $30 kit at most department stores that sell a lot of mechanics tools. Detaching the door of the mail box will simplify the process.
If you can remove the door — you might have to pop the hinge off — simply clamp it down on some workbench, ideally a drill press, and use a hole saw to cut a bigger hole that encloses the smaller hole entirely. If you're not a complete bastard, you will try to take into account the resulting look of the mailbox.
If you can't take the door off, or if you can but do not have access to a drill press, you can "practice" on a small square of thick plywood, then affix it to the door, like some template, and use it as a pilot for the handheld hole saw. Clamps will help secure the template to the work, otherwise a precisely cut template can often fit naturally around the door recess, allowing you to cut the hole with the door closed. Makes cleanup easy as most of the metal shavings will be inside the box.
Speaking of cleanup, protect surrounding surfaces with plastic bags and masking tape + paper. It simplifies picking up metal shavings. Treat vacuuming carefully, as portable units could accidentally blow fine metal dust all over the place.