Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 27, 2021	Feb. 29, 2020	Feb. 27, 2021	Feb. 29, 2020
Accumulated Other Comprehensive Income (Loss)
Balance at beginning of period	$ 798.3	$ 844.6	$ 643.0	$ 719.2
Foreign currency translation adjustments	10.8	(1.9)	45.9	2.5
Other Comprehensive Income (Loss), Securities, Available-for-Sale, Unrealized Holding Gain (Loss) Arising During Period, after Tax	0.0	0.0		0.0
Net current period other comprehensive income (loss)	18.6	(7.8)	57.3	(7.3)
Balance at end of period	850.1	836.8	850.1	836.8
Cumulative Translation Adjustments
Accumulated Other Comprehensive Income (Loss)
Balance at beginning of period			(56.0)	(48.3)
Foreign currency translation adjustments			42.8	2.5
Reclassification from accumulated other comprehensive loss - Other, net			0.0	0.0
Tax benefit			0.0	0.0
Net reclassifications			0.0	0.0
Net current period other comprehensive income (loss)			42.8	2.5
Balance at end of period	(13.2)	(45.8)	(13.2)	(45.8)
Pension and Other Post-retirement Benefit Plans
Accumulated Other Comprehensive Income (Loss)
Balance at beginning of period			(59.2)	(45.0)
Other comprehensive income (loss), net of tax before reclassifications			0.0	0.0
Reclassification from accumulated other comprehensive loss - Other, net			4.5	2.5
Tax benefit			(0.8)	(0.4)
Net reclassifications			3.7	2.1
Net current period other comprehensive income (loss)			3.7	2.1
Balance at end of period	(55.5)	(42.9)	(55.5)	(42.9)
Unrealized Gains on Available-for-sale Securities
Accumulated Other Comprehensive Income (Loss)
Balance at beginning of period			0.1	0.0
Other Comprehensive Income (Loss), Securities, Available-for-Sale, Unrealized Holding Gain (Loss) Arising During Period, after Tax			(0.1)
Reclassification from accumulated other comprehensive loss - Other, net			0.0	0.0
Tax benefit			0.0	0.0
Net reclassifications			0.0	0.0
Net current period other comprehensive income (loss)			(0.1)	0.0
Balance at end of period	0.0	0.0	0.0	0.0
Interest Rate Swap Agreement
Accumulated Other Comprehensive Income (Loss)
Balance at beginning of period			(18.9)	(0.9)
Other comprehensive income (loss), net of tax before reclassifications			11.1	(12.0)
Reclassification from accumulated other comprehensive loss - Other, net			(3.3)	0.1
Tax benefit			0.0	0.0
Net reclassifications			(3.3)	0.1
Net current period other comprehensive income (loss)			7.8	(11.9)
Balance at end of period	(11.1)	(12.8)	(11.1)	(12.8)
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss)
Balance at beginning of period	(98.1)	(93.7)	(134.0)	(94.2)
Other comprehensive income (loss), net of tax before reclassifications			53.8	(9.5)
Reclassification from accumulated other comprehensive loss - Other, net			1.2	2.6
Tax benefit			(0.8)	(0.4)
Net reclassifications			0.4	2.2
Net current period other comprehensive income (loss)			54.2	(7.3)
Balance at end of period	$ (79.8)	$ (101.5)	$ (79.8)	$ (101.5)