Would a five speed tranny out of a late eighties-early nineties 5.0 mustang fit behind a 390? I realize that the transmission may break, but I need a decent priced manual tranny that will work for now, even if I have to baby it.  

Advanced adapters may make one.  

There's no mays about it, a T-5 out of a late model Fox Mustang will never hold up behind a 390.

If you're looking for a decent priced manual trans to put behind your FE motor, I'd say hunt around the junkyards for an early to mid 70s Ford 1/2-ton truck with either a 3 or 4 speed trans that you can easily get a bellhousing for and bolt up to your 390. For what you'd pay to get a T-5 and the proper bellhousing and equipment to put behind your 390, this would be the cheaper option, and you wouldn't have to "baby" it.

Another option is to find a T-10 or Super T-10 to put behind it.