If Newegg says the warranty is five years, just verify the warranty status with Seagate when you get the drive. Seagate has a web form to check the warranty status.
There have been occasional reports of drives coming from Newegg AND other retailers that are large-system-builder OEM drives. These have NO warranty from Seagate. That's why it's best to verify the warranty once you get the serial number. If there's any problem with the reported warranty, Newegg will, doubtless, fix the problem for you. Just double-check when you get the drive.
P.S.
I've read that Seagate is changing its OEM drive warranty terms soon.