Business Segment Information - Reconciliation of segment income to entity income (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
Feb. 28, 2025	Feb. 29, 2024	Feb. 28, 2025	Feb. 29, 2024
Business Segment Information
Operating income (loss)	$ 71.1	$ 33.0	$ 112.2	$ 96.6
Pension settlement charge				(26.7)
Losses related to sale and exit of business	(64.0)	(1.0)	(65.3)	(2.6)
Other expense, net	(0.1)	(0.2)	(0.4)	(0.3)
Interest expense	(18.5)	(11.9)	(56.6)	(23.9)
Interest income	0.4	0.6	1.4	1.6
Income (Loss) before income taxes	(11.1)	20.5	(8.7)	44.7
Operating segments
Business Segment Information
Operating income (loss)	80.4	52.1	200.7	132.3
Operating segments \| Parts Supply
Business Segment Information
Operating income (loss)	45.4	31.1	107.1	74.6
Operating segments \| Repair & Engineering
Business Segment Information
Operating income (loss)	19.0	11.5	62.9	31.9
Operating segments \| Integrated Solutions
Business Segment Information
Operating income (loss)	9.6	8.6	23.8	22.7
Operating segments \| Expeditionary Services
Business Segment Information
Operating income (loss)	6.4	0.9	6.9	3.1
Corporate and other
Business Segment Information
Operating income (loss)	$ (9.3)	$ (19.1)	$ (88.5)	$ (35.7)

Sum of operating profit and nonoperating income (expense) before income taxes and noncontrolling interest.

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Sum of the net result for the period of deducting operating expenses from operating revenues, and the entity's proportionate share for the period of the net income (loss) of its investee (such as unconsolidated subsidiaries and joint ventures) to which the equity method of accounting is applied.

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Amount of gain (loss) from sale and disposal of integrated set of activities and assets capable of being conducted and managed for purpose of providing return in form of dividend, lower cost, or other economic benefit to investor, owner, member and participant.

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Amount of interest expense classified as nonoperating.

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Amount before accretion (amortization) of purchase discount (premium) of interest income on nonoperating securities.

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Amount of income (expense) related to nonoperating activities, classified as other.

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Amount of noncash expense (reversal of expense) for pension benefits. Excludes other postretirement benefits.

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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