I found Livingstone/Victoria Falls a good budget option.
You won't get all 5, but Chobe has hippos, giraffe, lions, buffalo, crocodiles, and quite a few elephants.
Plus the added bonus of seeing Victoria Falls. Low water in November, but still an impressive sight.
I took a one-day safari with Kalahari tours which was great ($150 USD) and included transport to and from Livingstone. Didn't have time for more, but if/when I go back I'll probably look at them first.