Before I comment, I want to briefly add a quote from Phil's post above:
Phil Stevens wrote: ... if done correctly.
Phil's post above is excellent, and I just want to play on it. I raise cows, not sheep, but they're similar as they mostly graze ground growing forages and browse a little shrubbery and tree leaves. One difference they have in direct impact to forages is cows only have one row of front teeth, and they pull forage into their mouth with their tongue, then bite and pull. Sheep have two rows of front teeth and can bite closer to the soil surface than a cow. This means sheep have the potential to overgraze a paddock worse than cows, even possibly denuding a soil.
Like Phil's post, it's all about management, and keeping the animals on the move. Some say it takes three days for a grazed grass to begin regrowth, and that's the number I use on my farm. During the growing season, my cows are in a paddock for three days, then I move them. Always. Even if there is what appears to the eye to be ungrazed grasses which some of my neighbors may interpret as "wasteful". It is anything but that. By me moving my cows, all the forages in a paddock get to rest, allowing time to not only regrow above the surface of the soil, but to also store carbohydrate energy in their root systems for the next grazing. Grass regrowth energy comes from stored energy in the roots, and it's very important to allow time (generally three weeks but it varies) for a grass to build back up the energy stores in their roots after a grazing. Failure to do this results in weakened grasses or in a worst case scenario from repeated overgrazing is grass die-out. Nature will rapidly fill the void of dying grasses with other things, sometimes things that grazing animals don't want to graze. Rotational grazing done correctly, which is allowing for rest, stimulates grasses and other forages such as legumes to spread and improves pastures.
On my farm, I move my cows every 3 days, and it is usually 4-5 weeks before the cows have run a full circle circuit and are back grazing the first paddock again. In the spring when cool-season grasses grow rapidly, my cows can't keep up so I mow to keep the grasses tender and higher in protein instead of letting them get stemmy and go to seed. In the summer, I don't need to mow the warm-season grasses to maintain anything.
There is another benefit to this type of rotational grazing I will mention, and it breaks the parasite cycles in grazing animals. Many adult parasites come out in animal poop, lay eggs in the soil, where they hatch and then the larvae crawl up grasses and other forages waiting to be ingested by a cow, repeating the cycle. If too much time lapses, the larvae die, thus breaking the cycle. Similar things with sheep too, but may I suggest looking into sheep parasite cycles to make sure rotational grazing is done accordingly to break those parasite cycles as I am not familiar with sheep parasites.
Paul Ladendorf wrote:With only 5 sheep per acre will they build the soil back up without other inputs?
It will build up the soil biology, but it will not increase soil mineral content. Soil biology is what makes soil minerals available for plants to use, so increasing soil biology can help make available minerals in the soil that are otherwise less available in lower biological numbers.
I assume I'll have to supplement their diet heavily.
Maybe not. I do suggest they have a mineral appropriate for sheep available free choice.