I think you are pushing s**t up hill wanting a 5 foot range.
It can be done but would require a BIG antenna coil and a lot of power to drive it. (like 3 foot square)
Not a very practical application for a door lock.
One source of information you could try is Texas Instruments, and run a few searches for the RFID frequency you need. as they have many dedicated chips and circuit information to suit.
I think you will find a 5 inch range will be more realistic for your project.
I have never worked with the 13.56 mhz range and know nothing about their limitations.
Pete.