Summary of Significant Accounting Policies - Contract Assets and Liabilities and Remaining Performance Obligations (Details) - USD ($) $ in Millions	3 Months Ended	12 Months Ended
	Nov. 30, 2022	May 31, 2024	May 31, 2023	May 31, 2022
Contract assets and liabilities
Contract assets - current		$ 123.2	$ 86.9
Contract assets - non-current		24.6	27.5
Deferred revenue - current		(14.7)	(19.7)
Deferred revenue on long-term contracts		(7.2)	(12.7)
Net contract assets		125.9	82.0
Change in contract assets - current		36.3
Change in contract assets - non-current		(2.9)
Change in deferred revenue - current		5.0
Change in deferred revenue on long-term contracts		5.5
Change in net contract assets		43.9
Change in contract assets		17.1	13.7	$ 1.9
Accounts receivable, net		287.2	241.3
Change in contract assets and revenue		17.1	13.7	1.9
Changes in deferred revenue
Deferred revenue at beginning of period		(32.4)	(30.6)
Revenue deferred		(311.1)	(267.0)
Revenue recognized		(319.9)	(257.8)
Other		1.7	7.4
Deferred revenue at end of period		(21.9)	(32.4)	(30.6)
Remaining Performance Obligations
Remaining performance obligation			$ 668.0
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2025-06-01
Remaining Performance Obligations
Remaining performance obligation (as a percent)			50.00%
Expected timing of satisfaction of remaining performance obligation			1 year
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2026-06-01
Remaining Performance Obligations
Remaining performance obligation (as a percent)			28.00%
Expected timing of satisfaction of remaining performance obligation			1 year
PBH contracts
Contract assets and liabilities
Change in contract assets		1.0
Contract Charges on non-achievement of minimum volume guarantees			$ 1.9	$ 1.7
Commercial power by hour, contract, amount derecognized from remaining loss reserves	$ 2.0
Charge related to early termination of PBH customer contract		5.2
Change in contract assets and revenue		1.0
PBH forward loss reserve		4.2
Air Line Customers | Termination Of Power By The Hour Program
Contract assets and liabilities
Termination charge		4.8
Change in contract assets		7.8
Change in contract revenue		7.5
Repair reserves		2.5
Obligation to purchase the rotable assets		5.5
Asset purchase obligation of purchase price		20.9
Accounts receivable, net		8.4
Contract assets with customer		10.1
Change in contract assets and revenue		7.8
Air Line Customers | Past Due | Termination Of Power By The Hour Program
Contract assets and liabilities
Accounts receivable, net		$ 4.1