OK, I tried to get a good view from a hill near by to the farmer's barn across the street. The hill top is 3.69 miles away and here are the views:
* - Standard View
* - 8x Zoom View
* - Binocular View
Note: I can clearly see the barn from the hill with standard view...small but viewable. The stored image on-line seems to degrade the photo quality.

The article that was listed here stated that a binocular could be used to see items from 5 to 10 miles away.
"The varieties of pocket-glasses may be used at distances of from five to ten miles. A glass known as the carbineer-glass is not larger in diameter than the finger, and may be carried in the vest pocket. (p. 231)" This would be good to identify the enemy in the distance but not used to identify strengths or unit types. Just spotting! That is what I was looking for. At what distance do you spot the enemy? This seems to cover it.
10 miles seems to be pretty far and would take some REALLY good binoculars but I could see 6 to 7 being achieved...with quality glasses. Above photos were take with a cell phone.
