Restructuring, Impairment, and Other Exit Costs (Schedule of restructuring and other exit cost reserves) (Details) $ in Millions	9 Months Ended
	Feb. 24, 2019 USD ($)
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	$ 66.8
Restructuring charges paid out of reserve, including foreign currency translation	14.7
Restructuring reserve utilized	(34.4)
Restructuring Reserve, Ending Balance	47.1
Severance [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	66.0
Restructuring charges paid out of reserve, including foreign currency translation	11.4
Restructuring reserve utilized	(31.2)
Restructuring Reserve, Ending Balance	46.2
Contract Termination [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	0.1
Restructuring charges paid out of reserve, including foreign currency translation	1.2
Restructuring reserve utilized	(1.3)
Restructuring Reserve, Ending Balance	0.0
Other Exit Costs [Member]
Restructuring Reserve [Roll Forward]
Restructuring Reserve, Beginning Balance	0.7
Restructuring charges paid out of reserve, including foreign currency translation	2.1
Restructuring reserve utilized	(1.9)
Restructuring Reserve, Ending Balance	$ 0.9