Is this going to be a hunting or non-hunting safari? These days I think $5000 could get you into a bare-bones 5-day plains-game hunt in Namibia, Zambia, or RSA. Non-hunting you that money would go quite a bit further. I'd personally avoid RSA- it's nearly impossible to find a non-canned hunt there these days. Zimbabwe is not a good choice currently, for obvious reasons.
If this is going to be a once-in-a-lifetime type trip, you need to make it Tanzania. Ive been around Africa, and Tanzania is
the wild place you dream about or read in Hemmingway. Late August in the Selous or Masailand you will likely see 500-1000 strong herd of Buffalo- quite a sight. They grow some big cats there too (one of which is now a my rug^^) The entire place just an order of magnitude more remote and unspoiled than the rest of southern Africa. You couldn't hunt Tanzania for $5000, but you could probably spend time there.
I would strongly recommend hooking up with your local safari club before deciding anything. You'll meet old-timers and professional hunters who have made dozens of trips to Africa in their lives. Their knowledge could save you a lot of grief, and believe me there is a lot of potential for grief in Africa. Don't travel there with some mickey-mouse outfit.
I also recommend the forums at www.accuratereloading.com
. It's the biggest online community of big-game hunters, but there is a wealth of knowledge there for non-hunters too.