We don't begin integration testing at day 0 of release, we are constantly integration testing.
That said, five days is a goal of ours, not a hard deadline or SLA. An example of this was the 1.5.2. This came out 8 or 9 days after upstream because we had failing integration and e2e tests starting a few days before release and it took some time to hunt down, address, and make sure it was an issue with how we're deploying k8s and not k8s itself.
Hopefully that clarifies how we're able to to stride towards that goal. To be honest, testing like this is as much and art as it is a science and it's taken quite a while to get to where we are now (and admittedly, still a ways to go until we're satisfied).
It also said "With recent updates to our build/ci process" but there is more to testing than continuous integration, especially for something as complex as Kubernetes.
In particular, continuous integration can run regression tests but how many bugs will it find due to interactions between features?
So you do not do any integration testing, or for that matter hardly any testing at all?