Make sure to take a look at this thread, probably it will solve your problem: Unreal Engine not downloading (Code: 5) - Installation & Setup - Unreal Engine Forums
" I enabled the debug logging on the launcher and started the download."
From your Dxdiag it looks like a couple of things are keeping your from installing the Launcher.
First, you need Windows Service Pack 1. That is a Windows update that is required in order to install the Launcher.
Also, unless you have another graphics card that isn’t listed, your internal card only supports up to Directx 10 and a Directx 11 compatible card is required in order to run the Launcher/Editor.
Here is what we recommend:
Desktop PC with Windows 7 64-bit or a Mac with Mac OS X 10.9.2 or later
8 GB RAM
Quad-core Intel or AMD processor
DX11 compatible video card