My TortoiseGit showed a strange behaviour: When I tried to push or pull, the window took exactly 5 minutes to appear. The commit window did not appear any more. Reinstalling TortoiseGit did not fix the issue. I used the git Bash as a workaround for some time until I found a fix: TortoiseGit was not able to write into its temp directory because the security settings (NTFS rights) were somehow messed up. For the C:\Users\MyUser\AppData\Local\Temp\TortoiseGit, I added my user with full access rights and everything is now working again :).

Hope this helps someone to fix this faster in case someone has the same issue.