This Error Code 0x800705B4 is commonly caused due to the .NET framework installation failure. These are following ways in which you can attempt to correct this error.

Disclaimers: Before you attempt to fix an issue with the windows update error 0x800705b4, we highly recommend you to take a registry backup and create a system restore point as a precaution method. In case if something goes wrong, we can restore your computer to the same stage and fix the issues. (In case if you not sure how to back it up, talk to an expert for assistance.)

Solutions for Error Code 0x800705B4:
This .NET Framework 3.5 for Windows 8 or Windows 8.1 won’t come with pre-installed .Windows 8, Windows 8.1 or Windows 10, and must be separately enabled to run applications that depend on it. So enable the .NET Framework 3.5 in Control Panel to avoid windows update 0x800705b4