The speed of HTML5 games right now is far more to do with your browser and its version than how good your computer is.
Firefox 7, Chrome 14 and Internet Explorer 9 all run HTML5 games excellently, and are getting even better. Older browsers are much slower, even on good computers!
So check your browser is up to date! If you're at work or a school and you're not allowed to update the browser, you can install Chrome and Firefox on non-admin accounts. So try installing a different one.