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The only engine options for an '02 Mustang were a 3.8 and three versions of the 4.6, no 5.0. Either way, the answer to your question is, unfortunately, no.
Actually, most Mustang transmissions--the ones without an integral bell--can be made to fit nearly any engine. But that does not mean they would be a good choice here, and you would probably need a different bell or an adaptor.
Your engine uses the same pattern as the 385 series, the 429/460. Thus, a ZF from a 460 truck can be used. This may require a hydraulic clutch, although I think 460s used an external slave set up (IIRC, CRS tonight)
Anything you like, if you buy the right bell housing. Figure $500 for a scatter shield, and they will drill it for what you want.
Otherwise, a Ford bell will have the Ford "butterfly" pattern. There are two depths, and truck transmissions like the NP435 or T18/19 will bolt up to one, and car transmissions like the top loader 4 speed or T5 will bolt up, although the T5 will require an adaptor.