I haven't heard this five-word rule. But I can easily think of many sequences of five words that no one would seriously consider plagiarism.
I think that I will
was the first time that
Britain, France, Germany, and Italy
all men, women, and children
March 1 of this year
turn left at the traffic light (that's six!)
five words in a row
If some university or whatever institution is classifying as "plagiarism" any use of five words in a row that have ever previously been used anywhere in the world, I think that every student there, not to mention every faculty member, is guilty of plagiarism.
You can't rationally define plagiarism simply in terms of the number of words that are the same. Many short strings of words like those above are the most simple and direct way of expressing a common idea. If you never heard one of those phrasings before, you'd be likely to invent it.
I'm reminded of a TV comedy I saw years ago where a writer of home repair books was accused of plagiarism. And so in court the other writer's lawyer read samples from the two books that were word-for-word identical. Statements like, "Attach the faucet using two screws." At one point the defendant says, "How many ways are there to say, 'Attach the faucet using two screws.' 'Put in the two screws to attach the faucet.' 'Screw in the faucet with two screws.' 'See the two screws? Put 'em in.'"
On the other hand I can think of many short phrases that surely would be plagiarism. Like, "I have nothing to offer but blood, toil, tears, and sweat." "The ultimate question of life, the universe, and everything." "In the beginning, God created the heavens and the earth." "I think, therefore I am." (That's only three words in the original Latin: "Cogito, ergo sum.") If you used one of those strings of words in a way that implied it was original, I think you would be guilty of plagiarism.