5x5x5 Last Layer parity? Wtf?

Yes it is an eastsheen. I just manually flipped one whole edge pair and one single edge piece (4 pieces total) and I solved it. But wait 9-4=5 that means 5 pieces were still out of place after I flipped 4. And 5 incorrect pieces wouldn't be solvable, would they?!?
 
I just manually flipped one whole edge pair and one single edge piece (4 pieces total) and I solved it.

It's also actually impossible to even do that. You said you flipped a whole edge group (3 pieces) and one extra edge piece. What type of edge piece was that... middle or outer edge? Because if you flipped another middle edge, it would not be solvable, however just flipping an outer edge alone isn't possible.
 
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