How old can references or sources in a thesis be?

References can be as old as they need to be to cover the material. I had some that were more than 30 years old. But if all of your references are "old," people are going to want to know why.

You must also be sure you cover the most current research in your field. A few in my own dissertation were for material published in the same year as my own work.

The link given in the comments and the revised question seems to be directed toward undergraduate research assignments, and the "ten years" reference is a part of an example assignment, not a requirement given by the Shapiro Library. The key idea in the link is that references must be "somewhat current."

For a thesis or dissertation, one must cover the field, including both early and very new research.

There is no rule about the age of citations. For example in my PhD-thesis I quoted some math-papers from 1600s that were originally written in latin (but those were exceptions).

Much more relavant than the year is the content of a citation and that you cover the relevant literature.

Also, you might want to include a few (relevant!) citations from recent years in order to show that you did your reading not just at the beginning of your thesis and then ignored everything afterwards.

I have cited a book on farming by Columella from the 1st century CE.

It provided crucial evidence for the use of a word at that time. But I did not take the evidence as the final say on the matter. I also cited 15th century academic analysis of the evidence as well as 21st century work. There is a fundamental difference between saying

It is true because X says so

and

X says so, so let us analyse it and cite more recent opinions on whether it is true.

In any discipline it may be necessary to contrast older and younger opinions on the same subject, and you will have to do some work yourself to argue that any given source, whatever its age, is - or is not - reliable.

As it happens, I rejected all the academic analysis and accepted my own interpretation of the original evidence. You as a researcher are expected to determine on a case-by-case basis what evidence needs to be cited, and what can be accepted.

Of course, at some stage, you have to accept that a certain claim is true because X says so. To do this you have to cite something that is fairly recent (which will depend on the discipline) and, if it not the most recent, argue why you are accepting it in preference to the most recent.