Mustang new car production started numerically from "100,000". There is no car #000,001 or 0005478. Your car is the 5478th vehicle built on THAT particular assembly line in 1964. Other type of vehicles (possibly falcons/comets/and maybe fairlanes) are also part of that #--depends on what was scheduled on the assembly line on what day. I don't know if the VIN's were differentiated as to the Mustangs being 65's and the other car's as 64's--did other Fords models have a 64 1/2 year too??????
If 2 cars are being built on 2 separate assemby lines, such as one in California and one in dearborn, it is possible that there are 2 vehicles with the same last 6 #'s. What differentiates the cars would be the 2nd letter of the Vin. R for California and F for Dearborn. 5R07F100000 vs. 5F07F100000 are possible VIN's, assuming that both facilities produced 64's. Another neat thing is that the assembly lines could start up months apart and and yet both could still use the same #, beginning at 100,000.
All in all, your car is considered a very early Mustang.