Hello! Yes, there are ways to jailbreak an iPhone 5c even if it is locked with an activation lock and the Apple ID has been forgotten. However, please note that jailbreaking your iPhone may void the warranty and can potentially cause security issues.
Before attempting to jailbreak your iPhone, it is recommended to try and recover the forgotten Apple ID or contact Apple support for assistance with the activation lock.
Assuming you want to proceed with the jailbreak, here are some steps you can follow:
1. Download a jailbreaking tool such as Pangu, TaiG, or Unc0ver on your computer.
2. Connect your iPhone 5c to your computer using a USB cable.
3. Backup your iPhone data in iTunes or iCloud before proceeding.
4. Disable Find My iPhone and any passcodes or Touch ID on your iPhone.
5. Launch the jailbreaking tool and follow the instructions provided to jailbreak your iPhone.
6. Once the jailbreak is complete, you can install third-party apps and tweaks not available on the App Store.
Please note that jailbreaking your iPhone may cause it to become unstable or even brick it, so proceed with caution and at your own risk. It is also important to keep your jailbroken iPhone up-to-date with the latest security updates and patches.