I am in Kansas and I have seen some holes dug out in the pasture that are approx 4-5" wide and I didn't feel inclined to stick my hand down it see how deep it is. What would be living in these? Any info would be appreciated.

Is there a mound to go with the hole? If so, probably a prairie dog. If not, wolverine, badger, sabertooth rabbit...

There is a small amount of dirt but not like a prairie dog.

If the holes are shallow, then my guess would be that a badger dug them trying to catch either mice, moles, or gophers. If there are several of these small holes in close proximity, then I would stick with badger trying to catch a meal.