I think this is going to be a question that keeps coming up time and again on this forum from now on. Companies around the world must have millions of courses created in software such as Adobe Flash or Captivate over the past 10 years and now that HTML5 has come on the scene all of these courses will either need to be recreated from scratch or else converted somehow to HTML5.
As to whether Cp7 is your answer...
Yes, Cp7 (and also Cp6) can create HTML5 content, but whether your mobile users will be happy with it is a different question. Captivate's HTML5 content does not include "responsive design" where the structure of the screen content changes according to the target device screen orientation or size. Cp has something called "scalable HTML" but it's not the same thing as "responsive design". Scalable HTML just changes the display size of the content, and there are quite a few bugs in that feature at the moment.
Cp6 can open earlier versions back to Cp4, upgrade the files to Cp6 format and then publish to HTML5. Cp7 can only open files back to Cp5. (Expect Cp8 next year will probably only open Cp6 etc). So, if your content was created in earlier versions of Cp (e.g. 4 or earlier) you may not have an upgrade patch unless you still have intermediate versions of Cp on your system which can be used to progressively migrate upwards to the current versions.
Lately I've been looking more at HTML5 as a platform for delivering e-learning courses. I can see it happening. But Captivate is still not quite there as yet.
One of the reasons this question will keep popping up, is the first news on the Captivate7 page. (See attached screenshot).
I have myself looked for info for some days, because some online computer magazine wrote an article that with Captivate 7, you could convert old captivate swf-files to html5.
It would have been a nice option where the project files are lost (we have some), and only the swf remains.
And if someone could give me HTML5 converter for Captivate 5.5, I'd be happy to test if it works or not.