I would think it needs to be 5" deep unless you are going with a smaller depth. Most of the recessed we looked at we're 5" and the opening was a little deeper than 5".

This one is 13.5 inches wide. It has a polished edge instead of a metal banded edge, though. The inside is plastic, with plastic shelves. It has a 17.5 inch high cabinet, so you will have to make your hole smaller. It is also only 3" deep. http://www.cabinetsmedicine.com/product/broan-nutone-b7233-focus-single-door-recessed-medicine-cabinet-2-shelves I would suggest that if you really want to replace the one you have with an actual medicine cabinet instead of using the methods others have suggested, you take it out and feel along the edges to see if you can easily widen your hole. Most cabinets are at least 14" wide. That half inch opens up a whole world of small cabinets to you. If the previous hole is not boxed with wood, you might be able to easily widen and lengthen it to suit a different cabinet.

Our medicine cabinets don't rust because they are simple wooden frames built into the wall, In the picture below, the middle mirror is fixed and the other two mirrors are the doors for the two cabinets. The doors are cabinet grade plywood with Blum hinges, and the each mirror sits on a nearly invisible piece of stainless steel trim and is held in place with mirror adhesive. Inside, the sides of the boxes are drilled so that adjustable plexiglas shelves can be set on pegs with whatever spacing is desired. This installation is 15 years old and is like new still. .

Never mind. Found a replacement, even though it's not a medicine cabinet (found a solution to make up for the lost storage space) . I can't delete my original post. A glitch? Going with this: