Brian,
You can find the build date of your GT by contacting a local Ford dealer and asking for an OASIS report. You'll need to provide them with the VIN (which can be found on the certification label on the driver's door), and from that they can tell you of any outstanding recalls, as well as the warranty start date and build date of your vehicle. As others have pointed out, there was a mid-year change in the 5-speed transmissions, from the T45 to the Tremec
3650. When you check the vehicle certification label, the transmission code should be a 'K' if it's the Tremec. Unless you have an automatic, in which case, ignore that last bit. :)
Hope this helps.