When I try to switch from a local account to Microsoft Account from PC Settings, I get through authentication and Microsoft login steps but at the end I get an error with the code 0xd000005e.

Can someone help ?

Networking configuration.

If you are going through a proxy, then this may work for you

run CMD.exe (as admin)

C:\windows\system32>netsh
netsh>winhttp
netsh winhttp>import proxy source=ie

btw, before using it, you should type your proxy settings in Internet Explorer. Good luck!

A Google search (http://www.google.com/search?q=error+code+0xd000005e&sourceid=ie7&rls=com.microsoft:en-US:IE-Address&ie=&oe=)is your friend for most of these error codes.