The problem is not the existence of 5TB hard drive. The problem is how do you carry a 5TB HD in and out from a NSA office. The places are highly guarded, and they'll monitor for everything that comes in and out. You might have some luck sneaking in small devices - like pretending you have a commercial CD, but it's actually a writeable CD - but sneaking in and out hard drives it does not seem possible. And if you do it with other medias (CDs, DVDs, zip drive) it's a LOT of external media to carry around.
I think you'd be surprised. There are a LOT of NSA offices connected to the same networks. Many contractors also have SCIFs installed in their own building that can connect to the government's internal security networks.
All SCIF computers are supposed to be logging any removable media attached to them. The fact that this wasn't even implemented after Snowden shows how incompetent the NSA is with securing its own systems.
There was a rumour that split privileges and no-lone-zones were to be required post-Snowden, but that is a huge burden to impose quickly, needs lots more highly cleared and highly experienced staff. I suspect this would be rolled out using technical measures as new facilities are designed, not possible to do all at once.
Should have been done 20 years ago. An intrusion detection switch and restrictive policies to lock down hardware access is all you need for a first line of defense. All 1990's tech.
Talk is cheap. Reality is that someone has to go to Capitol
Hill and ask for a billion dollars to secure the billion-dollar intel collection facility we just built.
And remember, even the best systems can be socially engineered. With patience and cash there is no door that cannot be opened.