Recently i was installing some new servers in my lab environment and ran in to this Windows Update error 0x800705b4.
Fix the Windows Update issue
Microsoft provides Windows Update troubleshooter which will detect the problem and (try) to fix it. Try using this method to fix the 0x800705b4 error.
Type troubleshoot in Cortana/Search at the bottom left corner of desktop.
Click Troubleshooting on the pop-up menu.
Click System and Security
Click Windows Update
Click Advanced to checkmark the **Apply repairs automatically, **click **next **to start.
If there are any problems detected Apply this fix