EA has just announced that The Sims 4 will become free to play for everyone in October. In the same Maxis announcement came news that the developers will host a "Behind The Sims Summit" live stream event next month to talk about the future of the series.

This has led to some rumors The Sims 4 has come to the end of its life cycle and a sequel will be announced next month at the Maxis event. The game is already eight years old and fans are excited for a sequel to the life simulation game.
Jeff Grubb has suggested, in his recent Game Mess Mornings podcast, that EA is getting ready to announce The Sims 5 and it could potentially happen next month. Grubb has had a good track record in giving out insider information. He predicted the Nintendo Direct this week. Albeit, his predictions about The Legend of Zelda: Twilight Princess and Wind Walker were off.
Everything we know that is related to The Sims 5
EA announced that The Sims 4 base game will be free to download. Not to mention, there's a live stream in October dedicated to the Sims franchise. Plus, a known insider just said that EA will reveal the next Sims game at the said event. Finally, there's the job listing by Maxis that details their need for a Multiplayer Game Designer.
TLDR; all signs point to The Sims 5 being announced sooner rather than later.
EA, on the other hand, assured fans that they will continue to support The Sims 4 after it will become free to play. The statement reads:
With The Sims 4 going free to play, our team is more dedicated than ever to developing new and meaningful The Sims 4 experiences for our players and we will continue to develop and release packs, kits and Sims Delivery Express drops into the foreseeable future.
Given the statements and events related to The Sims franchise, we can assume that EA is working on the sequel. It may be a long way off hence the statement from the developers that they will be supporting The Sims 4 for the foreseeable future.
As for the livestream event, it may just announce the roadmap for the soon-to-be free-to-play The Sims 4. Or we might get what we are hoping for in an announcement that The Sims 5 is coming. We will just have to tune in to the event to find out.