Below are several solutions to help you fix this error and get WSL working smoothly again.
This definitive tutorial shows you how to bypass a forgotten PIN Windows 10 by using the Command Prompt tool.
How to Fix WslRegisterDistribution Failed Error 0x80004005
Fix 1.

Set LxssManager to Start Automatically
Step 1.
PressWindows + Rto open Run, and then typeregeditin the text box and pressEnter.
Navigate to this location:
Computer\HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\LxssManager
Step 3.
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In the right panel, double-select theStartDWORD value.
In the value data box, type2and clickOK.
Reboot the computer and test whether the 0x80004005 error disappears.

Here are the steps.
TypeControl Panelin the Windows search box and pressEnterto access it.
In the upper right corner, set it to view all items by large or small icons.

Then clickPrograms and Features>Turn Windows features on or off.
Uncheck the option ofWindows Subsystem for Linuxand clickOK.
Step 4. reboot your box, and then re-turn on the Windows Subsystem for Linux feature.
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Are you bothered by the Windows Command Processor high memory usage issue?
Here are a couple of useful solutions.
Fix 3.
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Update WSL
Ensuring that you have the latest version of WSL can also help fix the WslRegisterDistribution failed error.
To update WSL, stick to this:
Fix 4.
Visit theWindows Subsystem for Linux download page, and click theInstallbutton to get WSL installed on your setup.
Fix 5.
Update Windows
Sometimes, WslRegisterDistribution failed with error 0x80004005 due to outdated systems.
You should always keep your system up-to-date to fix security vulnerabilities, address bugs, and enhance system performance.
Before proceeding with any system update, it is always a good idea to back up your important files.
Windows updates typically go smoothly, but sometimes unforeseen issues occur.
Or, you’re free to use professional backup software,MiniTool ShadowMaker(30-day free trial).
I hope the information above can help you a lot.