I come at this as a farmer, with a herd of cattle & more land in the cold climate of Minnesota, so take my thoughts for what they are worth, as applied to your very different situation.
A hay field is much nicer to cut, rake, and bale if it is long & narrow & very rectangular.
For your small amount of livestock on a small area of land in a warmer longer season, I would think you would be much better off grazing as much as possible, and buying your hay.
It costs in machinery to bale & store hay.
The livestock can harvest yours for free - once you get the fencing up. Pay for the hay - you'll be paying for it anyhow.....
If it were me, I would fence the other 5 acres, one long side is already fenced, so now you will have 2 pastures for about 1/2 ther money. In the future, you can split each pasture in 1/2 again with simpler wire and have 4 paddocks for rotational grazing. (You said a total of 5 acres of hay ground, not 5 acres total minus your yard minus your field, etc?????)
You don't have to go all out for rotational grazing, but having 2 or better yet 4 pastures will make you a lot more feed and better times. And less weeds. It's a good thing.
You can feed goats hay all year around, no pasture - but that _is_ the mudhole you are talking about, and is the most expensive way to do things. Use the pasture, imho.
As far as pasture shape, it doesn't matter so much, 1100 feet is no problem at all. It takes a lot more fence to make a long thing pasture is about the only negative, but if you already have 2.5 acres fenced that way, you are ahead of the game & go with it!
Oh - I just rered Muchigan, not Tennesse - but that's ok, I still stick with what I said, pasturing makes more sense than harvesting & feeding the hay.
Here is a very good beginner's guide to making hay:
http://www.sheepscreek.com/rural/haying.html
If you search his home page you should also find his equally good pasture FAQ, and one on preditors as well.
That should help you learn how much fert you need (soil test, adjust soil ph with lime if needed first,t hen add what is needed as you can afford it -planting legumes like clovers will help give you free N so you only need to buy P & K....) and how many bales or livestock you can get on your 5 acres.
Here in Minesota I can raise 20-35 head of cattle on a 9 acre pasture. Wow you say!!! But wait, I need to add a little grain every day over winter, and sometimes in summer. I fence off & graze an additional 2 acres of lawn (yes, lawn) around some of my buildings for about 2-3 weeks of hay, and I fence off a 5 acre oats field in fall that has re-grown with legumes, new oats, turnips, and so forth. Then in late fall they are out on 35 acres of cornstalks, grazing that.
I harvest about 10-15 acres of alfalfa or grass hay as well, in case winters are severe. I plan on them eating about 1/2 that, but you never know....
So to distill that, you could raise 10 head of cattle on your 5 arces with rotational grazing, but only for 5-6 months of the year in Michigan. You'll have to convert that into goats or sheep, I donno....
Small square bales are very, ery popular with smaller operations. they are easier to deal with on a small scale. Round or large square bales are easier to handle tons & tons of hay with big tractors. You will find both in Michigan.
Well, my reply rambled (see my handle???) all over the place, hope you can get something from it & ask more because of it.
--->Paul