Accumulated Other Comprehensive Income (Loss) - Schedule of AOCI Activity (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 28, 2022	Feb. 28, 2021	Feb. 28, 2022	Feb. 28, 2021	Nov. 30, 2021	Aug. 31, 2021	May 31, 2021	Nov. 30, 2020	Aug. 31, 2020	May 31, 2020
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	$ 1,185.3	$ 1,176.8	$ 1,185.3	$ 1,176.8	$ 1,210.0	$ 1,149.6	$ 1,182.3	$ 1,187.9	$ 1,147.4	$ 1,180.6
Other comprehensive income (loss) before reclassifications	1.6	6.3	(8.1)	22.7
Amortization of gains and losses, net of tax	0.2	0.1	0.6	0.4
Amortization of prior service (credit) cost (net of tax of $0.0)	(0.2)	(0.1)	(0.5)	(0.2)
Other comprehensive income (loss)	1.6	6.3	(8.0)	22.9
Ending balance	1,185.3	1,176.8	1,185.3	1,176.8	1,210.0	1,149.6	1,182.3	1,187.9	1,147.4	1,180.6
Amortization, Tax	(0.0)	(0.0)	(0.0)	(0.0)
Amortization of prior service credit, Tax	0.0	0.1	0.1	0.2
Accumulated other comprehensive income (loss)	(42.7)	(35.4)	(42.7)	(35.4)			(34.7)
Other Comprehensive Income (Loss) before Reclassifications, Tax			0.1	1.7
Accumulated Other Comprehensive Income (Loss)
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	(42.7)	(35.4)	(42.7)	(35.4)	(44.3)	(40.4)	(34.7)	(41.7)	(47.5)	(58.3)
Ending balance	(42.7)	(35.4)	(42.7)	(35.4)	(44.3)	$ (40.4)	(34.7)	(41.7)	$ (47.5)	(58.3)
Accumulated other comprehensive income (loss)	(42.7)	(35.4)	(42.7)	(35.4)	(44.3)		(34.7)	(41.7)		(58.3)
Foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Other comprehensive income (loss) before reclassifications	1.6	6.3	(8.6)	17.4
Amortization of gains and losses, net of tax	0.0	0.0	0.0	0.0
Amortization of prior service (credit) cost (net of tax of $0.0)	0.0	0.0	0.0	0.0
Other comprehensive income (loss)	1.6	6.3	(8.6)	17.4
Accumulated other comprehensive income (loss)	(38.7)	(32.6)	(38.7)	(32.6)	(40.3)		(30.1)	(38.9)		(50.0)
Retirement benefit plans
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Other comprehensive income (loss) before reclassifications	0.0	0.0	0.5	5.3
Amortization of gains and losses, net of tax	0.2	0.1	0.6	0.4
Amortization of prior service (credit) cost (net of tax of $0.0)	(0.2)	(0.1)	(0.5)	(0.2)
Other comprehensive income (loss)	0.0	0.0	0.6	5.5
Accumulated other comprehensive income (loss)	$ (4.0)	$ (2.8)	$ (4.0)	$ (2.8)	$ (4.0)		$ (4.6)	$ (2.8)		$ (8.3)