A web browser has never been a suitable test for HTML (or other similar languages). It doesn't point out errors, it makes (often horrible) guesses about how to deal with them, and frequently disobeys rules about
how things should be handled.
I'm guessing that you want a "validator." You could see if one of the trusted ones supports HTML5 and runs on Fedora. e.g. Try w3c-markup-validator.noarch
I haven't tried any HTML5 authoring, yet, I haven't had the need to go beyond HTML4, so I've not even experimented with it.