In case you didn't know already, iOS 13.5 is buggy (as is iPadOS 13.5). There's a particularly irritating battery drain bug -- MP4 playback is broken -- and some people's devices are stuck in endless reboot loops.
So much for "it just works."
But does the 13.5.1 release pushed out by Apple yesterday fix any of this?
Don't hold your breath.
Having installed iOS 13.5.1 and iPadOS 13.5.1, there doesn't seem to be any material changes. The release notes made no mention of any bugfixes, and my early impressions suggest this is the case.
This seems to be purely a fix for the Unc0ver jailbreak.
So, should you install it?
If you installed iOS 13.5/iPadOS 13.5, then you have nothing to lose, and this protects you against the jailbreak vulnerability. If you want to jailbreak, you need to avoid this update.
If you didn't move up to the 13.5 release, you could give this release a wide berth and possibly avoid the bug-fest.