HTML is at version 5.3 right now, There aren't "HTML5 Tags" and "non-HTML5 tags" in HTML, if it's an element HTML defines it's an HTML tag, if it's not…it's not HTML.
<p> is a tag in HTML, even in version 5.3, so how is it not an "HTML5" tag?
Today browsers read HTML, so if you're loading a site in HTML the chances are it's being read as HTML 5 unless you specify that it's some other language like an older legacy version of HTML, or XHTML, or something else.
As always - correctly mark up your content with the most-fitting elements that HTML supports, full list here: html.spec.whatwg.org
If you're confused about the right time to use a tag, read the spec, they have explanations and examples and it's a very helpful way to understand the right time and place to use any element.