As you may know, the 05C scheduled date means this was a pre-production car. It could have been built at any time from Fall '63 through March '64. A lot of the 05C cars were not built as a normal Mustang on the assembly line. They were test cars and/or special use. There are going to be some very unique details about this car depending on how original it is. You may be scratching your head when you run into them. I would hope that you spend the time to do some detective work throughout the car and document what you find. Look at all the date codes throughout, like glass, sheet metal, engine components, steering box. It will help ascertain better when the car may have been actually built.
There were approximately 200 or so unit number reserved for 05C pre-production designation. Cars with 09C are the official assembly line production start cars. The earliest unit number on an 09C car found so far is 100211.
Try not to do any restoration work at this time until you can determine what exactly you have. Also, do not throw anything away. You mentioned you swapped out the gas tank and radiator. Those are 2 very unique items that you may end up wanting to restore (if possible).
