Hi Hropt,
Can you bypass the Launcher and open the .exe file for the editor?
C:\Program Files\Unreal Engine\4.5\Engine\Binaries\Win64\UE4Editor.exe
If you can open the editor this way, then it is a Launcher issue. Please follow the link below and try the troubleshooting steps. If the issue persist, post your ‘Verbose Logs’. They will help us track down the issue.
If the .exe doesn’t open for you, please post back here to let us know.