More factions will come after launch.
It looks like EA and DICE will be following the same staggered content rollout strategy with Battlefield 5 that they employed to great effect with Battlefield 1. Responding to a fan, the Battlefield Twitter account said in (a now deleted) tweet that Battlefield 5 will only have the British and German factions available at launch- more factions will be added later on, via the Tides of War live service.
On one hand, I can see this giving pause and creating outrage in some quarters- that said, and believe me, I’m not among the first people to rush to EA’s defense usually, the updates for this game will all be free. We already know there will be no paid DLC. So you’re still getting the content, just slowly over time. It’s a lot like the strategy Nintendo leverages with Splatoon.
As for what the other factions might be? USA, France, Russia, Italy, and Japan seem like sure bets, given their prominence during the Second World War, but I am sure we will have more details regardless come E3.