In Visual Studio 2015 when you try to connect to GitHub you may get the message “Could not connect to GitHub.com”. The problem for this could be that you didn’t include GitHub extenstion feature during installation of the Visual Studio.
1. During installation of Visual Studio 2015 GitHub Extensions must be checked. (See following picture).
2. Even if you have included this feature in to the installation, you may still get the error. Actually, for some reason you cannot log in to the GitHub. In that case go to https://visualstudio.github.com and download the installer and reinstall the extension. That was worked in my case.
For instruction of how to install extension you can find on the web page.
Now you can open Connection from Team Explorer and choose GitHUb Extension.
The Login page for GitHub appears. Log in to the GitHub and start using GitHub.