Restructuring Initiatives (Schedule of restructuring and other exit cost reserves) (Details) $ in Millions	9 Months Ended
	Feb. 25, 2018 USD ($)
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	$ 85.0
Restructuring charges paid out of reserve, including foreign currency translation	(2.7)
Restructuring reserve utilized	(44.7)
Restructuring Reserve, Ending Balance	37.6
Severance [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	81.8
Restructuring charges paid out of reserve, including foreign currency translation	(1.8)
Restructuring reserve utilized	(43.0)
Restructuring Reserve, Ending Balance	37.0
Contract Termination [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	0.7
Restructuring charges paid out of reserve, including foreign currency translation	0.2
Restructuring reserve utilized	(0.8)
Restructuring Reserve, Ending Balance	0.1
Other Exit Costs [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	2.5
Restructuring charges paid out of reserve, including foreign currency translation	(1.1)
Restructuring reserve utilized	(0.9)
Restructuring Reserve, Ending Balance	$ 0.5