In DW, if you have a sufficiently new version of the program (I believe DWCS5.5 or higher)...
For existing pages...
1. Open an existing file
2. Modify > Page Properties > Title/Encoding
3. Change Document Type to HTML5
4. Hit Apply
5. Repeat for all current files in the site
For future pages...
1. Edit > Preferences > New Document
2. Change Default Document Type to HTML5
3. Apply. From there on out, all new pages will have that doctype when created.