I noticed that the top two speedruns for Rank 5 do not actually show the player achieving rank 5 and I was wondering why this is.
This is because while the in-game rank counter may only show 'Rank 4', the players actually did reach rank 5 because they reached the required amount of tips (that being $70.00).
The reason the game does not show Rank 5 is because the players did a double rank up by achieving enough tips to quote-on-quote "skip" a rank which had a lower amount of tips. For instance, the first place run had $43.74 at rank 3 on day 4, which was not enough to reach rank 4. However, by getting enough tips from customers and getting two bronze medals from Cooper and Kingsley (the two first-day customers), which give $9.00 each, they managed to get a total tip amount of $70.02, which is enough for rank 5, so rank 4 is "skipped." However, Maggie, the customer unlocked after achieving rank 4, will still be unlocked the next day.
For clarification, all of this is done to skip a day, which saves major amounts of time (about 3 minutes). Most runs will be completed in six days, but by "skipping" the rank, the run can be completed in five days.
Hope this helps clear up the confusion!