Are you planning to check in 5 pieces of luggage? Bicycle box and 4 separate panniers? Have you looked at how much that is going to cost you? I don't know of an airline who won't charge you an extra $150+ for each additional bag after 2. Who are you flying with?

Put the panniers into the bicycle box.
Put the contents of the panniers into a single bag ... something foldable. Perhaps even something with backpack features.