To be honest, I am more interested in contextual examples in which we cannot replace the words "specific" and "particular" with each other, keeping the intended meaning intact. Of course, the examples that we can replace them with each other in a synonymous manner are also welcome!
Added. I've realized that this previously asked (and now closed) question, "particular" vs. "specific", is in a way similar to my question. Thus, I try to explain what I have in mind to better direct the answers I am looking for. Somewhere else (in my writings) I've made a distinction between "the number 5" and "a number, say 5", thinking of the former 5 as "specific" since the five-ness of five matters, the latter 5 as "particular" since the five-ness of five does not matter. My question (here) is looking for "everyday" examples of this distinction.