Yes, there will be a Fallout 5. Bethesda's strongman Todd Howard confirms to IGN that the story of life after the nuclear disaster will continue. But it will take time.

First, of course, Bethesda will get Starfield, and then The Elder Scrolls 6. That game is currently in "pre-production", so it will probably take several years before Skyrim sequel is released. And as another cloud of concern (if it's mainly a new Fallout you want from Bethesda) is that they have some other ideas in stock. This is what Howard says:

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Yes, Elder Scrolls 6 is in pre-production and, you know, we’re going to be doing Fallout 5 after that, so our slate’s pretty full going forward for a while. We have some other projects that we look at from time to time as well.

So long wait. As usual from Bethesda. The latest Elder Scrolls game, Skyrim, was released eleven years ago. Fallout 4 came out in 2015 and the much-loved (uh) multiplayer spin-off Fallout 76 landed in 2018.