Right now the cap number the League cares about is the Top 51. So you have to account for 2 additional players on the eventual regular season roster. You also have many of those low end deals on players #54-65 currently under contract. All the PS guys are on future contracts. So the Top 51 may be closer to the Final 53 that it might first appear.
$5-7 might seem high (Packers seem likely to have 9 draft picks if comp picks come in as predicted) but that number is usually north of