There is no doubt that a hefty stack of five-gallon buckets warms the heart of every true do-it-yourselfer—their usefulness is practically limitless, so the more you have the better. Unfortunately, those big stacks are sometimes their own worst enemy because the increased weight of more buckets tends to push them more tightly together. Pulling on them only seems to exacerbate an already "sticky" problem—rather like the old Chinese finger puzzle! Understanding that a vacuum seal is the problem to overcome provides the only clue you need to unstick them easily.
Knock over the stack of buckets—do not be gentle (they are not likely to break). The resulting jar will often be enough to loosen them from one another.
Turn the stack on its side and press firmly downward near the open end of the topmost bucket to break the vacuum seal, while simultaneously pulling on the handle to slide it out. Repeat for each subsequent bucket.
Drill a small hole in any bucket that does not need to be airtight or watertight—this will allow air in to break the seal. If it still sticks, insert the tube from a can of compressed air (such as is used for cleaning computers) into the hole and spray air in to force them apart.
Twist them apart by securing the bottom bucket and turning the top bucket as firmly as possible to release the vacuum.