Cut "square" nails actually go back to about the 1790's. I can't quite tell from the pic, but yours look like cut nails. Most of the dug ones I've seen like yours are from early to mid-1800's sites, but these kinds of nails were in use probably until about 1880 or 90, maybe 1900 depending on the part of the country. The barbed wire is probably not from the same time period as your nails.
There are a lot of early sites with newer barbed wire, just because they used these places for several generations.
5" square nails are worth keeping if you find nice ones like that.