Can we Use HTML5 Even if Users Have Outdated Browsers?

The only outdated browser is IE (6/7/8) where in you can support HTML5 Semantics using html5shiv/html5shim even you can emulate some of the HTML5 API's using Polyfills.
There you go with the extensive list of all the PolyFills available @ https://github.com/Modernizr/Modernizr/wiki/HTML5-Cross-Browser-Polyfills Using polyfills you get almost the same user experience but with a performance hit hence one should always use Progressive Enhancement concept to provide the better web.

No we cant use it.
because html5 introduces new tags.Even the major browsers like crome,explorer,firefox are not having full support for html5.So if you try to use html5 in outdated browsers,your application will not show its expected behavior.It will show the html5 tags are not supported for your browser.It cause problems to display elements in that browser.

No you can't, unless you will use some javascript libraries that help you to support html5/css3 in outdated browsers like modernizr (http://modernizr.com/), HTML5 Shiv (http://code.google.com/p/html5shiv/).
But please note that these plugins may not give you full support as modern browsers, it will be buggy little and you will need to take care of differences.