From working on a Mayflower lineage for someone:
When using the Five Generation/Silver Books they may actually have a 6th and 7th generation in them for some lines. It sometimes took until those later generations to verify the 5th.
When doing a person’s line we only had to submit proof for the last 4 or 5 lines. They accept the first 5-7 generations which have already been documented in the Silver Book series. This speeds up the application process.