For example, I am told that anything 20 years or older is less credible than something, say, five or ten years ago. Is that relevant in a field that may not be studied as often as others, and thus is one of the few works written on the subject matter?
The issue I have now is that I own two books: A History of Their Own (written by Bonnie S. Anderson and Judith P. Zinsser), and then Barbara Tuchman's "A Distant Mirror".
I've looked on here and the consensus seems to be that the latter is filled with inaccuracies that are no longer considered true of the time period she is writing in, historical fiction or otherwise, yet the book is recommended for those with an interest in that period of history by various people.
Both of these books from what I can tell were published in the 80s...which is a long time ago. This brings me to my current issue. I have no idea how to tell where I should begin or which sources would be considered credible (primary is usually the best).
Thank you in advance.
For the most general answer...there is no hard cut-off date. The general assumption is that more recent books will have up-to-date research, but that depends very heavily on the person or persons doing the research and writing. Just because a book is written in 2020 does not mean it is more accurate than a book written in 1920, if the person doing the writing is simply regurgitating old sources without looking at them afresh, or without considering any research that has been done in the previous 100 years.
Assuming there has been any research in the last 100 years, which for very obscure subjects there might not be. And assuming too that you can in any way get away from the older source, which is not always possible. To give one example from my own field, the five-volume set of H. P. Lovecraft's Selected Letters from Arkham House is, to be generous, a severely flawed production: published from 1965 to 1976, the contain excerpts from 999 (or 1,000, depending on how you count) of Lovecraft's letters and postcards. All of them have been abridged, some have been further edited and censored, and a few contain misprints or straight out errors in dating and page counts. Nearly all of the contents have since been reprinted in unexpurgated form (where possible) along with many other letters that had previously been unpublished, so that the Selected Letters is almost redundant.
Almost.
Because there are still several letters that have not been republished, and can only be found in the Selected Letters, and the SL remains the main source for many of the quotations among Lovecraft scholarship. That's the problem with really impactful books: it's hard to get away from them entirely until the contents have been entirely superseded, and even then they have historiographical value.
So yes generally speaking newer books are (hopefully) more credible than older books, but it's very much an issue of needing to evaluate them on a case-by-case basis.
One thing to look at would be a recent dissertation in your field of interest, not so much for the text, but for the sources they used. Doctoral students are required to be systematic in their review of the literature, so a current dissertation represents a good look at what someone trained in the field thought was important to read and to cite. You can also look at book reviews in scholarly journals of new books on your subject-- that's where you'll get a sense of how the academic community views current scholarship.
I read Tuchman's "A Distant Mirror" long ago, but if I were to recommend a book on the 14th century today, last year's work by William Caferro "Petrarch's War" would be the kind of place I'd start. Caferro isn't doing anything like the breadth of the survey that Tuchman is, rather its a very deep dive into Florence at the time of the Black Death. In reading Caferro's work, you get both "the story" as he understands it, and his abundant footnotes, which tell you which sources he used and what he thought of them. He's spent a scholarly lifetime in the archives with original materials; Tuchman worked almost entirely from secondary sources (sources which in many cases were already quite old when she accessed them).
So: if you know little about a subject, it generally makes sense to read current scholarship first. As u/AncientHistory has noted, we all have cause to go back to much older sources-- in Islamic history, there are a lot of _secondary_ sources that are a century old that are still the best thing on the topic; sometimes a book from 1950 is the most recent work on your subject. One clue to a scholarly work's continued relevance would be subsequent reprints. So, for example Gustave von Gruenebaum's works on Islam from the 1950s have been reprinted fairly recently . . . evidence that they're still considered books that academic libraries and readers (his only audience) think are valuable.
But starting out with a current dissertation, looking through the sources they used, looking through academic book reviews (accessible on JSTOR) . . . that will give you a reasonable idea of the current state of play.