Take a look at Rulon Jones' Ranch in Idaho. My neighbor shot a 300 inch bull two years ago there. He said it was 10,000 acres mountains, horseback and high fence. He said he never saw the fence line. There is also a larger portion of the Ranch that's free range. .Not my type of hunting, I'm a DIY public land archery Elk hunter, but it is in your price range and trophy expectations.
Rulon also has a ranch in Utah. Broadmouth Canyon Ranch (both Utah and Idaho). I went there in 2014 and killed a 374" bull. The Utah ranch is over 20,000 acres and there is a 5000 acre Preserve. Very nice folks. They have management hunts that are reasonably priced (you can do it for the $5000 you mentioned. I can't tell you how many of those bulls I saw but some of their management animals are huge. Meals and lodging are included. the license is an extra.
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