You could probably get away with 20 or so in a 6'x2'x2' or 2.5' tank, which equates to 180 or 225 gallons respectively. I would tend to agree that a the 5' tank is probably a little small for a group that size. If you have the tank and so that is definitely the tank you are going to use then I would suggest cutting your numbers to around 8-10. I kept my group of 6 in an 80 gallon and it just ended up being way to small after I got them in there. You are only allowing each adult discus approx. 7.5 gallons per fish in the tank you are proposing. Even in the largest tank scenario I gave you above you are only giving each fish 11.25 gallons of water. Also on the note of the tank I would strongly suggest you get the tank drilled with overflows so you can set up a serious wet/dry filtration system. They need very clean water, and this will help to facilitate that.
Even though Discus like angelfish will enjoy a taller tank they will still spend the majority of their time hovering around their driftwood. In the wild large colonies of discus live in this way. The dominant fish will live up amongst the roots and driftwood with less and less dominant fish being further and further from the "safe" area. So the more dominant the fish is the more it will hang around the drift wood and decorations in the tank, with the less dominant fish being forced out into open "unprotected" areas. So you will want to invest in some really nice pieces of drift wood IME. They also enjoy planted tanks but I would stick to primarily tall large leafed plants like amazon swords that will shade the bottom of the tank from the bright light that will be needed to grow the plants. Giving you the best of both world, a dimmer tank, and the shelter and shade provided by the live plants, along with the nutrient export benefits.
They like warm acidic "tannin stained" water. So RO/DI water will be very benificial to keeping your water stable in the low ph ranges that you will want. Peat moss is a good addition to the filter body for its ph lowering ability as well as the tea color it will give the water, which will relax and calm the discus. Some owners don't like the look of it, but the fish prosper in it. Also the water temp should be around 82 vs 78 for most other cichlids.