The idea behind HTML5 is to offer one complete solution for web development. HTML5 has many features which integrate technologies like Flash directly into the HTML protocol. This streamlining process is critical considering both Adobe and Google will soon stop supporting Flash for mobile devices.
HTML5 unifies the web and apps will work across all devices which saves companies money as they now only need to build one website or app and don't need different options for different devices. Where SEO is concerned, all back-links can now go to one place.
HTML5 is the most up to date and all encompassing way of web developing and people need to switch over to HTML5 sooner rather than later to stay at the cutting edge of the design world.
HTML5 in a lot of cases may mean that redesigns are necessary to keep up to date with the rest of the world but, once it's done, it is done so therefore HTML5 is the way forward.
Most browsers now fully support HTML5 but some legacy IE versions still do not. This is only a problem in the short term though until everything catches up.
There are only a few reasons to not switch to HTML5 and by changing over early you are both keeping with the times and streamlining your development processes.