Criticalmass, thanks very much, great info.
Yes 5 miles is negligible for a long sea voyage at ship speeds on a very big ocean.
As you said celestial nav for aviation had to be replaced due to a number of factors as time and technology moved on.
The WW2 eg I mentioned before, night nav over a blacked out Europe would rely heavily on astronav with a possible 5-10nm radius of error for airborne fixes as opposed to approx 5nm at best when stationary on the ground at a known location. With only these fixes usually avail to update the airplot and all the compounding errors caused by varying winds, accuracy of flying heading and airspeed etc these would of cause often cause very large errors in establishing a ground position and thus led to very, very, poor bombing accuracy.(hence "Area Bombing" as a result).
Even 1-3 nm is a huge amount when trying to hit a small cluster of buildings in a large city, like a factory complex or a small village for eg. A very big problem in those days before other methods were developed to improve position fixing at night in bad weather.
I will let all you knowledgeable "old sailors" finish this interesting discussion . Great to see this "art and science" is being kept alive by at least a few around the world.