I’d say no. That’s 5000 people who are told they might have cancer while in fact they don’t and who will then undergo further testing that is at best traumatic and at worst extremely invasive if not outright damaging.
Take intestinal cancer, for example. You can get screened for that and if you screen positive, they will take a biopsy - a fairly unpleasant and not entirely risk free procedure. Then it gets worse. If the biopsy shows some part of your intestines isn’t quite in order (a likely outcome, though not necessarily one that indicates cancer) they will take out that bit of intestine, just to be safe. This is a very invasive procedure and because it’s your intestines we’re talking about, you digestive system will be seriously out of whack for a while - if it ever heals completely - seriously and significantly degrading your quality of life. All this for a, let’s use your figures, 1 in 6 chance that you might have had cancer.