Depending on the configuration of the plot, and the zoning of the land, on 5 acres, you MIGHT be able to legally hunt on that land. I would recommend using a shotgun (I'm guessing your LONGEST possible shot on the property would be 200yrds, since most 5acre parcels are 110yrds x 220yrds). A .22lr or .22WMR with very carefully chosen shots might be another option.
What are you ultimately trying to accomplish? If you're trying to knock out coyotes and foxes in your horse pasture, then snaring is a good alternative to trapping, as are body gripping "conibear" traps, if legal in your area. On a smaller patch like that, I'd hang snares under the fenceline where the game trails are crossing under the fence, run baited conibears on some of the interior game trails where the horses can't really access them, and maybe put down a FEW footholds along the game lines where the horses can't access them at all.
Snares are relatively easy to prep. I make all my own snares, but pre-fab snares can be bought at most outdoors/hunting shops. These need to be "weathered" for a few months outside (simple process: boil them in water, then leave outside).
Traps need to be boiled and waxed to prevent corrosion and freezing. These would need to be inaccessible to the horses.
Beyond all that, you need to be a little more specific? What do you know, or not know, that you're asking about?
One KEY point to keep in mind, if your neighbors have dogs, then trapping on your land is likely going to be a bad idea. Even if you catch a dog in a foothold, it tends to make the neighbors upset. God forbid you kill their dog in a snare or conibear.