Yes, you can validate both in the official W3C website:
- HTML and more: http://validator.w3.org/
- CSS: http://jigsaw.w3.org/css-validator/
- Also RDF: http://www.w3.org/RDF/Validator/
For HTML HTML5 though, you might get best results at http://html5.validator.nu/ because it's usually updated as the standard is. I believe this might be official for the WHATWG standard of HTML5. It also has a few more options.
The HTML validator is for HTML 2 to HTML5 (including XHTML 1, 1.1, and various profiles; HTML5 is a little experimental though, but it's probably the best for XHTML5.), RDFa, any custom XML* language with an embedded DTD, MathML, SVG and SMIL. The CSS validator goes up to level 2 and some of level 3.
*(possibly any custom SGML language with an embedded DTD and SGML prologue. I remember playing around with this, but I think I barely scratched the surface with SGML.)
Sometimes the validator for HTML can be very slow though. It wasn't always like that and it might've gotten better since I last checked. I haven't been using it to check CSS as often as I used to, so I can't speak on how well it's doing now. On its bad days, you might try the validator at http://www.cssportal.com/css-validator/