I was a bit confused at first but things are pretty clear now. It's your hedge and (stray branch notwithstanding) entirely on your property. And at 5ft high it's shorter than a fence (hardly a nuisance).
Sorry Kybosh - I think you're pooched on this one. You've try to be reasonable but the neighbor clearly doesn't agree with your thoughts and feels justified by their actions. A second polite attempt (with slightly increased intensity) MAY be a good option but I think it's probably best to go straight to the "Legal" arguments.
I've dug up a couple of quick links from the city.
City Bylaw on Trees and Shubs (Not much good info here, just a couple links)
City pamphlet (PDF) on Yard Maintenance (decent, help establish you're in the right)
City of Calgary "Good Neighbor" guide (give the guy a copy may really prove a point?)
Best of luck.