Error Code 0x800705b4 is common for all the Windows Operating systems when you try to install the updates. It usually appears when Windows 10 or Windows 7 update system is broken or there are network related glitches.
Usual causes for this error code 0x800705b4 are communication failure over the internet with Microsoft update servers.
Disable the proxy internet connection and try again to install the update.
The second case would be with your Antivirus. There are proxy settings enabled under your settings of any security programs that you may be using. If you cannot find the procedure to stop it, you can ask our techs on chat support to guide you.
There are failed windows update services that could also cause you this error 0x800705b4 while updating Windows.
Repairing Windows update services is not possible like you repair any windows apps from the add/remove programs. There is a procedure that you need to follow through command lines.
This requires the user to have administrator rights on his computer. As per the Microsoft set of rules defined on various Knowledgebase articles, the steps are simplified as mentioned here to reset your windows update services.
NOTE: Following these steps carefully will not make any changes to your personal data or programs. It will only reset the Windows update services.
For any additional support in fixing windows update-related errors like Error code 0x800705b4 or any, you can reach us on chat here to get instant Help and Support.