You could also try booting with just the internal HDD first. Once up and running, plug in the external HDD and see if the power supply can cope.
If it still fails to boot as soon as the Seagate is plugged internally to the SATA port, there could be an issue with the hard drive itself. Check it and format on a PC to make sure?
Booting your two HDD's at once could be an issue for the standard 2Amp P/S.
If your external 5Tb drive is not powered, a powered hub should fix the issue for you, as already suggested by Futeko.