I have used .net's webbrowser control. Unfortunately, it
is not supporting HTML5 or Complete JavaScript. When
I googled, many said that the control depends on IE
version installed in the machine. I have installed IE10.
Though it supports HTML5 (Even I checked the same
webpage in IE10 and it worked), the webbrowser
control in my application doesn't. In some forums, they
recommended to tweak the registry. How can I do it in
every Clients machine? Is there anything that can I do?

Horrible idea, if it depends on having internet explorer installed I would immediately close and click away, the front end should work on any modern browser on any operating system. You need to rethink this.

One workaround that doesn't require registry hacks is to embed the browser itself in a container control, like tab control.