I disconnected my battery (2005 Ford Mustang-V). Where does this red wire connect?

 

Under that red cover, probably. Most likely an add on power line for a radio/amp or something. It should just go under the nut on the end there, that's the purpose of that post. Here's a picture:


That post on the right in this picture. Assuming it's not been changed out/broken or something. In that case... whatever post you can stick it on will do, but I'd avoid the tightening nut on the left side. Also, I'd recommend some dielectric grease on that terminal (if not both) slathered generously to ensure no corrosion happens. Depending on your environment, of course, but it's not a bad idea...

That said... BE CAREFUL. If you don't know what that's for, and/or why it's disconnected, perhaps you need to investigate that before you start ***** nilly adding a power circuit to the terminal, fused or not.

Hope that helps, and welcome to the forums!