Restructuring Initiatives (Schedule of restructuring and other exit cost reserves) (Details) $ in Millions	9 Months Ended
	Feb. 26, 2017 USD ($)
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	$ 76.6
Restructuring charges paid out of reserve, including foreign currency translation	106.6
Restructuring reserve utilized	(62.6)
Restructuring Reserve, Ending Balance	120.6
Severance [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	73.6
Restructuring charges paid out of reserve, including foreign currency translation	97.4
Restructuring reserve utilized	(54.5)
Restructuring Reserve, Ending Balance	116.5
Contract Termination [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	1.5
Restructuring charges paid out of reserve, including foreign currency translation	0.9
Restructuring reserve utilized	(1.6)
Restructuring Reserve, Ending Balance	0.8
Other Exit Costs [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	1.5
Restructuring charges paid out of reserve, including foreign currency translation	8.3
Restructuring reserve utilized	(6.5)
Restructuring Reserve, Ending Balance	$ 3.3