What do you mean by "I don't know that any is wasted"? The water that goes through the system when it regenerates/cleans itself, goes down the drain and out. Sorry, I really don't know but am trying to learn.
Is water used flushing toilets, filling a swimming pool, watering the lawn in a desert, washing the car, or taking a shower wasted? That depends on your point of view.
OK. So your question is how much water is used each regeneration. The water is used during the cycles... Backwash could be 10 minutes at 3 gallons per minute. It could be 1 to 5 gallons for brine fill . It could be an hour of brine draw+slow rinse at 0.25 GPM. To know the numbers, you would either measure what comes out of the drain hose or it could be adding up the pieces. This would involve identifying the BLFC (expect a label near the brine hose) and the injector info (I don't know if that would be on a label or not). It would involve looking up the timings on your controller.
To actually measure the use, you could direct the brine hose into a set of 3 33-gallon garbage cans standing by. Move the hose quickly one to the other. Siphon out the garbage tanks when done. The brine hose can empty to a place well above the controller if it helps your siphoning later.
The 5600 is not an electronic controller (has no LCD display) such as the 5600SXT or 7000 would be. An electronic controller would let you change the various settings. You could find the service manual for your controller and that might tell some of the info. See
http://waterpurification.pentair.com/en-US/product/fleck/5600/ Resources. If you are motivated to see what you can yourself, somebody might be able to fill in the rest of the info.
I'd rather not unplug/disconnect my water softener but my city gives each home water limits about how much water can be used a month without facing a fine for excess water use, so that's the dilemma.
OK. Your new question could be how to minimize the water usage during a regeneration while still keeping the softener working. That could be done by changing settings in the controller. You would need the above info, plus you would need info on the the raw water hardness and the resin tank size.
What is your water use permitted before significant fines kick in? 100 gallons per day? 250 gallons per day? What?
One way to save water is to not run the water to let it get hot when you wash. One way to do that is to recirculate your hot water so that hot water comes out instantly, and the other is to use the water while it is still coming out at room temperature.
You could go to the laundromat to wash clothes, or you could get a newer washer that uses less water. You could do dishwashing by hand, or at least stop doing partial loads with the dishwasher.
If your toilets are not 1 gallon per flush, there is probably a "program" to pay for some or all of replacing your toilets. If you do replace any toilets, don't just go with whatever the program provides, but be willing to pay extra to get a 1 GPF toilet that will flush well.
You could get into "Navy showers".
https://en.wikipedia.org/wiki/Navy_shower Maybe make it a game. Learn to read your water meter, and keep score.