Big 5 game reserves in the Western Cape, South Africa
Often visitors to Cape Town would also like to see some real dangerous African animals in the wild. Obviously the lowveld (or Tanzania/Kenya) is the best place to have that experience, but time or money constraints sometimes makes this impossible. No need to despair, you can now see the big five on a day trip or overnight trip from Cape Town.
Where to see the big five near Cape Town:
Aquila private game reserve is well known, 1.5 hours away just before Touwsrivier
Fairy Glen is only 1 hour away near Worcester
Garden Route Game Lodge is 3.5 hours away past Albertinia, before Mossel Bay
Sanbona wildlife reserve for those with deep pockets is 3 hours away past Montagu
Gondwana game reserve is 4 hours from Cape Town, 30 km past Mossel Bay

Times stated are from Cape Town as stated on the web sites (optimistic in my opinion).
Hunters coined the term big five as these animals were the most difficult to hunt on foot: lion, elephant, leopard, buffalo an rhino.
Let me state up front that you will be very lucky to see the big five in a single short trip to most game reserves as you may not always see lions and leopards. In the small private reserves you can see these animals, although not necessarily all of them in the wild.
If you are not set on seeing the big five, there are many other game and nature reserves you can consider. You may even be able to see the little five. In order to promote the small animals, people came up with the little five: Leopard Tortoise, Rhinoceros Beetle, Ant Lion, Buffalo Weaver and Elephant Shrew.