Sending a letter to everyone within 5 marks does seem a little optimistic, almost trying to play the system.
It's one thing to look at those within 5 marks if they were below the predicted grade and check if a mistake is made, it's another to suggest that it's worth checking as a blanket rule. It will give false hope to far more people than is fair-the majority don't go up and obviously we hear far more about the person who went up 9 marks (and remember it better too) than the person who stayed the same or went down one mark.
There's also times when the grade boundaries are close enough together that they could be closer to the lower boundary, in which case it's irresponsible to suggest that to people without warning them how close they are and that grades can go down as well as up.
I'd say within 1-2 marks fair enough to give it a go, especially if you need the higher grade.
3 marks or more, if you had a reasonable expectation a higher grade, and don't have reason to think it was a bad paper, then it's worth asking to see the papers, check the marks were added correctly, that they haven't missed a question etc and have someone to look over to see if there are potentially questions that have been mismarked.
Over the years, we've asked for two reviews of papers, one GCSE statistics, and one A-level Further Maths, which were 1 and 2 marks off respectively. Both went up, which could give a false idea of how easy it is to go up.
But both dd had already looked at and seen where she thought there were the extra marks. She also looked at her GCSE history and concluded that although she thought the marking was harsh, it was within the limits and wouldn't go up, so we didn't put it in for review.