As an intermediate solution, while there is no dedicated HTML5 player in Moodle yet, consider using JW Player filter we have developed:
https://github.com/lucisgit/moodle-filter_jwplayer
Notice, that JW Player is not free for commercial use. The filter does not include JW Player code, you have to obtain one from their website, or use the cloud version. In either case you have to accept terms and conditions. The installation instruction is included.