Will there be a season 6?
If there is a season 6, then the development should already be started. It'd take a few months to get enough content for the season, like 2 new maps (if you consdier the current season content with one new map and a reworked map) and some new weapons. But so far DICE have said nothing and it's worrying. If they do end the support after season 5, I guess they won't say anything until the very end of season 5 to not to upset the player base.
I really hope they can continue the support though. The live service is doing a great job for each season. The player base is increasing with PS plus and latest steam sale with free play. The game is in a very stable state and they should keep the momentum going till the next BF title. The end of support of BFV was a huge let down. It'd be a shame if EA is making the same decision again.