You can get all the information about iOS 15.5.1 Jailbreak from this page.
Zeon iOS 15.5.1 Jailbreak
Zeon is the only jailbreak solution for iOS 15.5.1 and iPadOS 15.5.1. Zeon Jailbreak working on every iPhone and iPad Devices running 15.5.1
How to use Zeon Jailbreak to Install Cydia?
Step 01. Install Zeon Jailbreak from here
Install Zeon Jailbreak
Step 02. Once Download, open it from Home Screen to run Zeon Jailbreak
Step 03. Tap the Cydia button to install
Step 04. Now you can use Cydia to install Tweaks / Themes / Games / Widgets
Best Cydia Repos for iOS 15.5.1
Once you have jailbroken the iOS 15.5.1 version, you should add trusted repos for iOS 15.5.1 Cydia.
So here it is the most popular and trusted repos for iOS 15.5.1 version.
Cydia Repos for iOS 15.5.1
ShowLive ( ShowCuts ) for iOS 15.5.1
With this method, you can add Cydia widgets to the Lock Screen and Home Screen without Jailbreak.
ShowLive supports every iPhone model that runs iOS 15.5.1. But ShowLive does not support for the iPadOS Models.
Install ShowLive
AltStore for iOS 15.5.1
AltStore IPA Sideload method supports iOS 15.5.1 running iPhone and iPad models. So with this method, you can sideload Jailbreak IPA / Cydia IPA .
AltStore needs Windows or macOS computer to install. After then you no need PS support to sideload IPA files.
Install AltStore from here
Best Third-party App Stores for iOS 15.5.1
This is another method to install Tweaks / Themes / Widgets to your iPhone and iPad Devices. When you search for the best Tweak app store in Google, it will suggest websites. So you have to check these websites one by one.
So your easy reference we listed all the best app stores on one page. You can install any app store from this page as you wish.
Install Tweak App store for iOS 15.5.1
Glance App for iOS 15.5.1
Glance is another Jailbreak free method that supports changing the Lock Screen. But Glance App does not support for change Home Screen.
Also, Glance does not support the iPad Devices.
Install Glance
Taurine Jailbreak for iOS 15.5.1
Taurine jailbreak is the only tool that works on iOS 15 versions. According to CoolStar, 90% of progress is done and ready to release once complete rest of the work.
So if you want to use Taurine Jailbreak for iOS 15 versions, do not update to the latest versions because Taurine jailbreak only supports iOS 15 to iOS 15.2 Beta ( According to Developer Tweet messages )
Also, Taurine jailbreak does not support to installation of Cydia because Sileo is the default package manager for Taurine.
Checkra1n Jailbreak for iOS 15.5.1
When checkra1n was released initially, the developer said Apple cannot patch it from the iOS update.
But still Checkra1n failed to jailbreak iOS 15 / 15.0.1 / 15.0.2 / 15.1 / 15.1.1 / 15.2 / 15.2.1 / 15.3 / 15.3.1 / 15.4 / 15.4.1 / 15.5.
At this time, the checkra1n jailbreak tool only supports iOS 14.8 version.