Business Segment Information - Sales by Segment (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Nov. 30, 2024	Nov. 30, 2023	Nov. 30, 2024	Nov. 30, 2023
Business Segment Information
Net sales	$ 686.1	$ 545.4	$ 1,347.8	$ 1,095.1
Inter-segment Sales
Business Segment Information
Net sales	24.2	23.2	49.6	44.6
Total Sales
Business Segment Information
Net sales	710.3	568.6	1,397.4	1,139.7
Parts Supply
Business Segment Information
Net sales	273.7	227.6	523.4	464.4
Parts Supply | Inter-segment Sales
Business Segment Information
Net sales	2.7	1.8	5.2	2.6
Parts Supply | Total Sales
Business Segment Information
Net sales	276.4	229.4	528.6	467.0
Repair & Engineering
Business Segment Information
Net sales	228.8	145.4	446.4	282.9
Repair & Engineering | Inter-segment Sales
Business Segment Information
Net sales	21.2	22.1	43.8	41.6
Repair & Engineering | Total Sales
Business Segment Information
Net sales	250.0	167.5	490.2	324.5
Integrated Solutions
Business Segment Information
Net sales	163.4	156.6	332.3	312.9
Integrated Solutions | Inter-segment Sales
Business Segment Information
Net sales	0.3	(0.7)	0.6	0.4
Integrated Solutions | Total Sales
Business Segment Information
Net sales	163.7	155.9	332.9	313.3
Expeditionary Services
Business Segment Information
Net sales	20.2	15.8	45.7	34.9
Expeditionary Services | Total Sales
Business Segment Information
Net sales	$ 20.2	$ 15.8	$ 45.7	$ 34.9