You can download the iOS 15.5 or iPadOS 15.5 beta on your iPhone/iPad by navigating to Settings -> General -> Software Update. The update will only show up on your iPhone or iPad if the developer beta profile is installed. If you are in the public beta channel, you should get the update within the next 24 hours.
iOS 15.5 could very well be the final point release of iOS 15 before iOS 16 is released to the public in September. Apple has already announced that it will be hosting WWDC 2022 through June 6-10, where it will announce iOS 16, iPadOS 16, and the next version of macOS.
Alongside iOS 15.5 beta, Apple also seeded the first beta of watchOS 8.6 and macOS Monterey 12.4 to developers.
At the moment it is unclear what changes iOS15.5 packs, but we will update this post as and when we come across some major changes.