Well, the amount of enjoyment entails not only the hunt, but how much I enjoy eating the kill; therefore, it is tough to beat quail or pheasant with good dogs. And which is why waterfowl & doves don't make the top 5. Upland birds are fun in the field, and mighty mighty tasty fried up later.
Elk and turkey talk back to you, which is exciting, and taste very good, so they'd be tied for 2nd.
Feral hogs is the poor man's grizzly, and don't taste too shabby, so that'd be third.
Sandhill crane (yummy) & deer are up there, but deer are crafty and require a lot of patience and time - can be very frustrating at times.
I've not tried sheep, goats, and similar, but I'd imagine they'd be very exciting, provided you don't die of a stroke or heart attack trudging around the mountains.
Quite sure that nothing would beat the adrenaline rush of dangerous game like elephant, hippo, cape buff, leopard, lion, but gotta save up for that trip.