Can I use HTML5 to build my pages and still be able to use Perl + mod_perl effectively?

mod_perl and pretty much any other component you can think of (PSGI, which you should really consider, web frameworks like Mojolicious, Catalyst and Dancer, etc.) are all agnostic to output format. You can use them to deliver JSON, PNG, PDF, HTML, plain text, HTML 5 or any other format you want.

What else would I need to consider?

If the actions on the server side take more than about 5 seconds, you need to think about how to execute them in the background, and provide feedback to the user when the action finishes. This article should give you the basic understanding on how to do such things, though there might be more modern tools available for doing it.

I don't think the generation of (draft) HTML5 as opposed to HTML4 or XHTML makes any difference to the dispatching mechanism. It will matter only in the content of the templates you use.

"Can I use HTML5 to build my pages ...."

IMO (YMMV), the question should be "Should I use HTML5...?"

"Can I" is likely to ignore issues such as 'production readiness' and 'market (user) acceptance.'

In that case, by all means explore HTML5. But realize that you are not following the path already laid, but helping to lay the path! The HTML5 website points out strongly that anyone trying to use the draft without also belonging to the discussions will find it shifting out from under them.

So sign up with that group and participate in the discussion. Explore some open issues in your experimental code, and share the results with the group. Not only will you get a grade, you will make real contributions to the project!

What kind of Master's is it? Mine was all math, like spending a whole semester following one complexity proof.

HTML5, of course, is merely a means of expression.   And, “the web page” that you are describing is merely a user interface to a much larger and more complex “back-end” system.

The back-end system that you are describing might have been, in earlier days, described as “a batch-processing system.”   Or maybe, “an application server.”   Be very mindful that a suitable system probably already exists, and that it most certainly will also have a web-based UI available.

You are definitely in the “requirements definition” stage, having not yet even begun the due-diligence that needs to happen to consider all of the relevant implementation options that you or this project might have.   You are, therefore, a long way (IMHO....) from being ready to consider questions of Perl, mod_perl, and/or HTML5 ...

In fact, it is rather profoundly important at this stage to bear in mind that “this is not the Starship Enterprise.”   No matter where you may happen to be going, you are not “boldly going where no man has gone before.”