You weren't specific really but a Toyota (RAV4, Highlander, 4Runner...) would do the job very well and maybe a Subaru, especially if its a manual transmission.

Tundra, Subaru w/manual, an old Nissan Frontier w/manual....just depends on the use you want it for.

5k is a pretty low bar for AWD vehicles these days. So the answer really depends on what trade offs you are willing to make. High miles?  Cosmetic issues?  Needed fixes?

2 suggestions. (opposite sizes)
1) older Subaru Forester. Might find one with low miles

2) pre-2000 suburban. As long as it wasn’t used for towing, those things could go 250-300k miles and you can get them for a song. Parts are pretty easy to find. Watch for rust

1.) You can get a first gen 2000-2006 tundra for under $5000 if you look hard enough. The tundra was their first full size truck and they built them extremely well. Only problem is the low mpg, but you can just stick a Dolant cold air intake to improve it's mpg.  

2.) highlanders are great family cars with pretty nice awd systems

3.) 2006-2008 rav4 v6 (not I4- burned oil)

4.) 2004-2006 honda crv

I reccommend the toyota rav4 because it is great all around. The toyota tundra requires expensive maintnence with the v8 though