What's the best way of doing this? I have a client that wants to rewrite their site that was originally done with flash to have the same animations working on iPad/iPhone etc. Can I use Flash CS5 and export to HTML5? Has anyone been asked to do something similar?
No. Adobe has not yet publicly released a version of Flash that exports as HTML5. They have previewed this feature, but it was not part of the CS5 release.
There is a small possibility that Adobe will announce such a feature next week at Max, but no guarantees that it will be released until CS5.5
So, you will need to build the new site from scratch. The tools you should use are dependent on the content of the original animation.
My studio has been doing a decent amount of this type of work over the past few years. It is really a balance of HTML/CSS/JS (mostly using jquery) and we have learned a lot about the canvas tag.
All of the studio's work is code based (we don't use the Flash timeline) and, because Actionscript and Javascript are "sister-languages", we have found that we have been able to cut and paste some of our functions from As3 directly into JS with little rewriting.
Animations have to be a bit simplified (performance is ok, aliasing on rotated graphics drives me crazy as there is no native smoothing) and browser testing is a real challenge (our work has to support IE6) but it is definitely possible if the client has the inclination (and the budget).
In my opinion, it would be cheaper (and better) to design a new site optimized and designed around what HTML5 does well than to simply port something made for Flash into HTML5.