Essentially any of the ones that do HTML, do HTML5. It just added a few tags to the specification. Programs let you type in any tags you want to use. It's just up to the designer to know what they're doing.
If you want to move to something more designed for the web then Espresso, TextMate, Coda, Textwrangler, Eclipse, Netbeans, and even Dreamweaver are suitable for the task.