Battlefield 5 will not have a Premium Pass. Maps, modes, or anything that might divide players will be free, including events that will be run as part of BF5's new months-long Tides of War chapters.
What exactly will be for sale after Battlefield 5 releases hasn't been announced in detail, but EA has assured us that anything you can buy, you can earn by playing, and that players won't be able to buy an "unfair gameplay advantage"—so we're talking about cosmetic items only, presumably. According to a statement to Polygon (opens in new tab), there will be no loot boxes, and only cosmetic items that have no gameplay impact will be sold. They'll also be unlockable with in-game currency.
Head here for everything else we know about Battlefield 5, including details on all the new systems, modes, and more.