Can I Save a 5.1.4 project then open it in 4.7

There was no change regarding this part of the process between v4 and v5. Is it possible that your problem is not really the assigning of footprints but the library management. Anyhow here a few tutorials that will help out:

Or are you unsure how to do it inside the symbol editor? (Here the interface did indeed change quite a bit) In which case: