It's possible to put a newer 5 speed trasmission on a 91 mustang gt v8
If you are just wanting a newer T5, any FOX type T5 will fit.
The 92 & 93 are the same as your 90/91 except they have the carbon-fiber synchros and the reverse brake feature enhancements.
The 93 COBRA T5 will fit just fine and adds the tapered pocket bearing on the input shaft.
A 94/95 GT T5 is the same as the 92/93 except for the input shaft and bearing retainer. These can be retrofitted for a clean interchange.
A 94/95 COBRA T5 is the same as a 93 COBRA T5 except for the length of the input shaft and bearing retainer. These can also be retrofitted.
A94-98 V6 T5 will FIT with the input shaft change, but the internal gears are weaker than a 90-95 GT. The gears 1-4 in this T5 are the same as an 86-99, except, of course, for the length of that input shaft and retainer.)
A 99-04 is not a good swap because the crossmember mount is in a different place and the speedometer sender is all-electronic. The gears inside these ARE a match for a 94/95 GT.
If you are thinking about a T-45, a 3650, or a T-56 you would need a custom bell housing to fit the 5.0 because these were made for the 4.6. There may also be some clearance issues with the transmission tunnel in a FOX.