Peel Out

time for a look see in the diff

yea

Pretty sure a limited-slip differential was standard on all Mustangs packaged with a 5.0L, regardless of whether they were manual or auto. Only Fox bodies they seemed to be optional on were on Lincoln Mark VII models, but most of the LSC trim models got 'em. (I don't recall any T-birds or Cougars having stock limited-slip, except for maybe the TurboCoupes and SuperCoupes.)

Do a rear gear fluid change, look for shavings and things amiss in the rear assembly while you've got the cover off, and be sure to use some limited-slip additive when you refill. Might get lucky and catch it early enough that you can get by on it as-is for awhile before it comes time for a rebuild ... and a set of 3.73 or 4.10 gears.