I think you'll have trouble finding the Grand Vitara or Toyota Rav4
for less than $5K unless you're willing to accept a vehicle with high miles.
The Suzuki Sidekick is available for well under $5K, but the vehicles
are generally from the early 1990s.
The Kia Sportage fits the budget, and can be found with more reasonable miles.
The knock on the Sportage is that there are very few aftermarket parts. There's a
web site called
www.upyourkia.com that sells spacers for suspension lift.
The Sportage ground clearance is 7.7 inches with the stock 205/75 R15
tires, 27 inches in diameter. The Kia enthusiast group on 4x4wire.com
say that 225/75 R15, 28.3 inches in diameter, will fit without modification.
But there will be a bit of power loss with the larger tires.
Here's the link to the Sportage group on 4x4wire
http://www.4x4wire.com/forums/postlist.php?Cat=0&Board=UBB70&page=0