I am thinking about getting an iMac and really want a 27" 5k but I only have around 19" of height within my desk. I have plenty of width, it's just the height. I need to lover it an inch or so to fit. Is this possible?
Yes, the VESA mount model is a choice for you http://store.apple.com/us/buy-mac/imac-retina-vesa
You have to purchase a mount to go with it, and you can't return to the normal foot if you would want to in the future. You do also have to decide how it will be mounted, either with a clamp, or holes in your desk, or mounted directly to the wall.
Another option would be to get the normal iMac 5k, and modify your desk to allow the foot to be mounted underneath the top of your desk (somehow), maybe with a shelf built under the desk surface. I've seen a couple of folks that did that, cutting a hole or slot to allow the iMac foot to rest on a lower shelf.
(Just an idea that I have seen before. It's a "project", however, and you might not want to modify your own desk in that way.