So I'm realtively new to flying.  If FAA "guidelines" for hobbyists state you must maintain sight of your UAS then what is the benefit to owning one that can fly over 1 mile away?  Can flying 5KM away be done, especially if you have automatic object detection, and avoidance, on the drone?  And does it matter if I'm on a private farm/property that spans 5 miles away without obstruction?  Does the guideline only refer to public property, given that I'm not near any airport either.  Thanks for your opinions in advance.

You won't ever hear from the FAA or anyone else if you are flying on private property that spans that large.  Just don't break the 400 foot altitude limit.
Since there are now so many birds being flown now with many in heavy populated areas, and suburbs, that is why the LOS is so important.

In your case, fly like the wind!

I don't think you will ever get to 5KM with obstacle avoidance turned on, you would need sports mode.  Also, at 5KM you will have difficulty seeing helicopters, birds of prey and other things that may be a hazard to your aircraft.  In good conditions, most people can see most large flying things at 1KM, helicopters probably at 2Km, beyond that you are taking bigger risks and for a hobbyist you probably don't have a good enough reason to take those risks, even if it is unlikely that a helicopter will ever fly over your farm.

As you are new to flying, you would probably have difficulty dealing with an encounter with a helicopter when you can only see it via an LCD screen that will probably be looking in the wrong direction most of the time, and at 5Km will probably not receive a continuous and error free video stream!  

You don't have to fly long distances to have fun, there are plenty of challenges at close quarters.

If your flying for farm purposes then do things properly and get the appropriate permissions.

Even if you own your farm, you don't own the airspace above it, anyone and everyone has the right to use that airspace, you have to share it and obey the rules.

I agree with Microyb over Nigel, if it's your land your flying over have at it under the 400' limit. And you ask about having a drone that can fly over the LOS range. Can't your car go over the posted speed limit? Don't you sometimes go over the posted speed limit, I do ? If your asking does that make it legal? Probably not.