HTML Tidy seems like a powerful tool although I am having a hard time to find from their docs whether they do simple validation (I guess it does given that you ask the question).
This html5validator gives you a simple yes/no answer whether some files are HTML5 valid. It is based on the same backend that powers https://html5.validator.nu/.
It can be integrated in continuous integration. The README contains example configurations for TravisCI and CircleCI.