How you would get rid of the bodies would depend on your local environment and the rate at which they appear. Any disease that first causes sickness, gradually weakening the affected over a day or more would cause the sick to congregate at medical facilities, and as soon as these overfill, at home.
Its not realistic to assume all 95% who will eventually die will be dying over the course of a few days, more likely it will spread out over weeks, if not month. Even highly contagious diseases do not infect everyone on first exposure. Take the outbreaks of mostly harmless flu as an example, it usually lasts month, even in highly populated areas.
This means the majority of bodies will be immediately discovered, and as soon as the scale of the pandemic becomes obvious, authorities will work to deal with it. As the pandemic progresses, more and more people will die at home (medical facilities become overrun on the first few days). Even if 2-5% of the initial population would die per day, collecting the dead bodies (especially under martial law) is relatively manageable logistically. All you need is a truck and some people to go around a neighborhood to collect the dead. Most likely these will be accompanied by armed soldiers and not delivering dead bodies will be dealt with as a crime under martial law.
Once collected, the bodies can be disposed of by any means locally available: by burining in waste disposal facilities, mass graves or even by dumping in landfills. While 7 billion sounds much, in terms of weight and volume its not so much compared to the amount of waste we have to manage annually anyway. Its just a very busy year for the garbage movers.
At some point, when the death toll has climbed high enough, civilization will break down and organized disposal of the dead would come to a halt. Its hard to imagine at which percentage this would happen exactly, from a standpoint of pure work force, there is no reason why this couldn't work even until only the 5% ultimately surviving would remain. But realistically it would break down at some point, psychological effects of mass death on this scale are hard to imagine.
I'd say the amount of bodies isn't the major problem, the main problem is maintaining order and organization. As soon as the society falls back to savagery things really go downhill. The best chance of survival then is in rural areas, there are fewer people to begin with and more resources (food, water). Considering that there will have been a phase where the dead have been disposed of orderly, there wouldn't be too many corpses to deal with in rural areas.