Yes, HTML5 will have an effect on SEO. Any fundamental change to common mark-up will have an effect on SEO and with greater support for HTML5 specifications by browsers site owners and webmasters should consider utilising HTML features sooner than later.
HTML4.01 published in late 1999 by the W3C is SGML based and is a formatting language used for structuring and presenting content on the web. HTML5 is the next iteration of the HTML specification worked on by the WHATWG since 2004 and basis of a W3C group since 2007 and still in working draft.
HTML5 takes into consideration the developments on the web with additional support for media and introduces a number of new elements some of which semantically describe replacements for common page blocks amongst other things. I see some distinct similarities to some of the new tags in HTML5 as with the Microformat 2.0 drafts for hMedia, hNews & hAudio which help to segment specific types of data/assets for which there is continued support for by search engines.
What’s of great interest with HTML5 is how it will help search engines segment a webpage when analysing it. We already know that search engines utilise complex alogithms to separate content from common page blocks such as navigation. Most of a web page content is wrapped in either a <div> or <span> tag whereas HTML5 introduces structural tags such as header, footer, nav, section and article. This can only help search engines to sort and return the most relevant content in results. As well as tags defining audio, video
Yahoo! in 2007 introduced the robots-nocontent attribute so that a site owner could help separate common page elements from the main content and the new tags in HTML5 will no doubt work in a similar way.
Once enough websites start using HTML5 search engines will inevitably start using these new elements to improve search results, so it stands to reason that site owners should start making incremental changes before such changes are announced by the likes of Google and Bing.