Reservation
R1000 pp including park fees. May be slightly higher for foreigners, since park fees will be higher.
Travel
Total: R2500 per person.
Flights (assuming from within SA) are about R750 on average one way. So R1500 per person return.
Taxi from and to the airport about R150 per person. So R300 return.
Accommodation: R350 per person per night at a local BnB. You could get away cheaper.
Gear
Total: R4000 if you're starting with absolutely nothing and want to buy everything.
I've only itemized the big stuff. But given an estimate on "My Recommended Gear" list. Most people will have at least some of the stuff, so this will depend on what you already have, can borrow, and how comfortable you want to be.
Backpack R1000
Stove R 200
Hiking Boots R 1000
Pots set R 300
Knife: R200
Sleeping bag: R800
Food
R 500 pp
See the food section for more details. But you're looking at hiking goodies costing you about R100 per day per person. An upper estimate, and one that might see you slightly more chunky after 5 days of walking and heavy lifting.
Total
R 8000.