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5.0L (1979-1995) MustangTechnical discussions on 5.0 Liter Mustangs within. This does not include the 5.0 from the 2011 Mustang GT. That information is in the 2005-1011 section.
When my TPS sensor was going bad my car did the same thing. I changed the TPS and problem solved. Im not saying this is your problem but wouldn't hurt to check.