Welcome to the forum. Looking at the "Mustang Production Guide, Vol 1", your VIN falls in early June for scheduled builds. There is some controversy as to the scheduled dates as Ford juggled a car's position in the line so the actual vs. scheduled "could" be off as much as two week (so they claim). Back to your VIN question, it falls around the 8th or 9th, with a June 5 and a couple of 6's VINs falling in the middle. The 7th is a Sunday so don't use that. To get a better feel, look at the date codes stamped on the fender aprons as fenders and hoods are easily replaced, re your door being replaced. The format of the date code would be similar to this: 05 28 2 which would mean May (05), 28 (day), 2 shift, no year is included. The code would be stamped into the horizontal surface on the fender apron between the cutout on the LH side and hinge. It's sometimes covered by the fender.
Good luck,
Jim