Apple’s activation servers are generally instant. I’ve gone through the official process maybe 20 times in the past two years for work, and it has never not worked within 1 minutes let alone waiting 5.
Here is the official guide and link for the previous user to remove that lock:
Activation Lock is part of the iOS Activation status here:
So if you believe it’s failing, the instructions there are correct - contact Apple Support directly. The only thing I can add, is Apple doesn’t tell you the full email of the previous owner, so unless you have the passcode, you won’t really know which email is “firstname.lastname@example.org” above.
- How exactly are you connected to the internet from the device to try and unlock / activate it?
- Do you actually know the email some other way or were you putting something hypothetical in the question?