Impossible? Nothing is....
This repair is actually quite possible. As a matter of fact, our shop does them quite often. It IS a VERY tedious task, but definitely not impossible. With the right tools, patience, and understanding of the phone mechanics and fragility, this repair can be completed by repairing just the glass. In regards to the amount of adhesive left on the LCD after glass removal, this can be broken down by using goo gone/orange glo and a toothbrush. Brush a very light amount of solution onto the lcd in a circular motion taking great care not to touch the edges of the LCD as this WILL leave an oily looking residue under the digitizer and it's not very appealing to stare at. Something else that we have learned is that you can actually remove the TOP LAYER of plastic off of the digitizer/lcd combo, leaving the screen looking near perfect. Bear in mind...there is a layer underneath the clear plastic that looks almost like a tint. If this is removed, the phone typically will not work anymore. So, take great care in making sure that you only peel up the plastic layer. Adhere the new glass to the plastic frame, lay the LCD behind it, bolt on the LCD backplate, and install. Most vendors provide 2 strips of adhesive with the new glass. You can apply this to hold the glass down, taking care not to cover the sensors or the camera. OR google iphone 5 UV Bonding Solution. This is the more technical option, but definitely hides blemishes on the screen better. Youtube iPhone 5 glass only repair, it's worth a try instead of spending 200.00 on a new assembly. Enjoy! Hope this helps.
-Tech Savvy