I'm surprised this doesn't really talk about the thing that was most obvious to me: assuming the 5 year survival rate is five years from diagnosis, that means that if a tumor is diagnosed earlier, even if the cancer kills you, your death is more likely to be outside the five year window.
So for example, if you have (hypothetically) an untreatable cancer that would take six years to kill you, if it is diagnosed right away, you would be counted as a survivor, but if you are diagnosed at year five, you'll only survive a year.
Tumour evolution and progression is complex, being diagnosed early does not guarantee a linear growth. Even when it's biopsied at a timed interval you can't get a full picture of the cancer (invasive pattern etc) evolution trajectory. In some cases low grade tumours will be put on surveilance without radical treatment.
Diagnosis is complex too, you don't want the test to have low specificity. False positive is sometimes tolerated.