Is there an XHTML5 (XHTML + HTML5)?

There is no XHTML + HTML5. XHTML was a path taken by W3C to try to restrict the entire Internet code pattern. The idea was for everyone to write valid and semantic code. HTML5, in turn, is a language update initiated by a group of developers linked to companies such as Apple, Google and Firefox.

You can write XHTML syntax (which does not have that much difference) in HTML5 quietly. The W3C validator will not complain about the syntax. But it's a great practice not to mix the two.

XHTML has a standard and is validated based on the older HTML, which does not include some new html5 inputs and some metatags syntax, unfortunately XHTML is based on HTML2, following its syntax and validations. it is very important for IDES and Servers to be able to validate your code, different from what you see today in PHP for example (I have developed 8 years in this language), q is that lot of gambiarra and bad code. With standard-based validation, a code that is readable by all is possible.  We look forward to a JSP definition with HTML5 syntax. Until then, it's all about the old XHTML, CSS and JQuery.

I find it interesting to understand what specification and implementation is.

XHTML 4.x, HTML5 are specifications, are a set of rules that define how HTML should be interpreted by browsers, is something analogous to the cultured norm of the Portuguese language.

Implementation is how browsers actually interpret, which generally differs at one point or another depending on the browser, is analogous to spoken Portuguese.

Historically XHTML did not paste, most browsers did not care much about the XHTML specification, largely due to some of the annoying XHTMl rules like having to set a doctype with a url that no one remembered, having to close solitary tags such as <br> that had to be written as <br /> according to the XHTML specification. For browsers it was more important to make the code that people wrote than to follow the XHTML syrup specification.

Based on this, HTML5 was created, which is a closer specification than browsers implement, which is what really matters.

It was mostly pressure from browsers to make a functional specification, but specifically from a group called WHATWG .

tl; dr: xhtml5 does not exist.