Business Segment Information - Sales by Segment (Details) $ in Millions	3 Months Ended		6 Months Ended
	Nov. 30, 2023 USD ($)	Nov. 30, 2022 USD ($)	Nov. 30, 2023 USD ($) segment	Nov. 30, 2022 USD ($)
Business Segment Information
Number of new operating segments | segment			3
Net sales	$ 545.4	$ 469.8	$ 1,095.1	$ 916.1
Inter-segment Sales
Business Segment Information
Net sales	23.2	20.3	44.6	42.4
Third-Party Sales
Business Segment Information
Net sales	568.6	490.1	1,139.7	958.5
Parts Supply
Business Segment Information
Net sales	227.6	183.6	464.4	352.2
Parts Supply | Inter-segment Sales
Business Segment Information
Net sales	1.8	2.0	2.6	3.8
Parts Supply | Third-Party Sales
Business Segment Information
Net sales	229.4	185.6	467.0	356.0
Repair & Engineering
Business Segment Information
Net sales	145.4	134.8	282.9	262.4
Repair & Engineering | Inter-segment Sales
Business Segment Information
Net sales	22.1	18.3	41.6	38.6
Repair & Engineering | Third-Party Sales
Business Segment Information
Net sales	167.5	153.1	324.5	301.0
Integrated Solutions
Business Segment Information
Net sales	156.6	127.3	312.9	255.1
Integrated Solutions | Inter-segment Sales
Business Segment Information
Net sales	(0.7)		0.4
Integrated Solutions | Third-Party Sales
Business Segment Information
Net sales	155.9	127.3	313.3	255.1
Expeditionary Services
Business Segment Information
Net sales	15.8	24.1	34.9	46.4
Expeditionary Services | Third-Party Sales
Business Segment Information
Net sales	$ 15.8	$ 24.1	$ 34.9	$ 46.4