Business Segment Information - Sales by Segment (Details) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 29, 2024 USD ($)	Feb. 28, 2023 USD ($)	Feb. 29, 2024 USD ($) segment	Feb. 28, 2023 USD ($)
Business Segment Information
Number of new operating segments | segment			3
Net sales	$ 567.3	$ 521.1	$ 1,662.4	$ 1,437.2
Inter-segment Sales
Business Segment Information
Net sales	26.1	33.9	70.7	76.3
Third-Party Sales
Business Segment Information
Net sales	593.4	555.0	1,733.1	1,513.5
Parts Supply
Business Segment Information
Net sales	242.3	227.6	706.7	579.8
Parts Supply | Inter-segment Sales
Business Segment Information
Net sales	2.3	14.0	4.9	17.8
Parts Supply | Third-Party Sales
Business Segment Information
Net sales	244.6	241.6	711.6	597.6
Repair & Engineering
Business Segment Information
Net sales	140.8	128.0	423.7	390.4
Repair & Engineering | Inter-segment Sales
Business Segment Information
Net sales	23.6	19.8	65.2	58.4
Repair & Engineering | Third-Party Sales
Business Segment Information
Net sales	164.4	147.8	488.9	448.8
Integrated Solutions
Business Segment Information
Net sales	165.5	143.5	478.4	398.6
Integrated Solutions | Inter-segment Sales
Business Segment Information
Net sales	0.2	0.1	0.6	0.1
Integrated Solutions | Third-Party Sales
Business Segment Information
Net sales	165.7	143.6	479.0	398.7
Expeditionary Services
Business Segment Information
Net sales	18.7	22.0	53.6	68.4
Expeditionary Services | Third-Party Sales
Business Segment Information
Net sales	$ 18.7	$ 22.0	$ 53.6	$ 68.4