The only remaining jailbreak tools for iOS 13 are unc0ver and checkra1n. The former is based on a software vulnerability and support the iPhone XS and iPhone 11, and the jailbreak method is relatively simple.
checkra1n is based on the hardware-level checkm8 vulnerability, jailbreak needs to operate under macOS, and support up to the iPhone X.
However, the downside of the software exploit is that it's unstable and gets killed with every update from Apple.
Now, Apple has closed the verification channel for iOS 13.5.5 Beta 1. In other words, users who have already upgraded to iOS 13.5.1 are no longer likely to downgrade, and iOS 13.5.1 can't be jailbroken by unc0ver yet.
Of course, as mentioned earlier, checkra1n ignores the software version and can still enjoy the convenience of jailbreaking as long as the device is an iPhone 5s~X.