>I have an ASP.NET application running with Set Compatiblity On. If I run that application under HTML5, this is all messed up. If I turn that switch off, everything is ok. This is mentioned at many places on the net that this switch should be turned off in IE because it gives this result. Is there a way to turn that switch off from our application or we have to tell all of our users to turn it off?

Have you looked into the meta tag that sets compatibility levels for a page (there are several options on this)..

<meta http-equiv="X-UA-Compatible" content="IE=EmulateIE8" >