With the 5 foot span I think simple sliding bypass doors would be a god idea. Glass is not expensive (if you have a glass shop nearby) and would up the appearance a bit.
Your top and bottom could me 30% thicker than your shelves so that dados could be milled into them to hold the doors. A little wax for lube, some slip on pulls and your done. This would also give you a clear view all the way to the bottom. Or there is this type of product in plastic or hardwood.
Any sufficiently advanced technology is indistinguishable from magic.
- Arthur C. Clarke