Business Segment Information - Sales by Segment (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
Net sales	$ 678.2	$ 567.3	$ 2,026.0	$ 1,662.4
Inter-segment Sales
Business Segment Information
Net sales	28.3	26.1	77.9	70.7
Total Sales
Business Segment Information
Net sales	706.5	593.4	2,103.9	1,733.1
Parts Supply
Business Segment Information
Net sales	270.7	242.3	794.1	706.7
Parts Supply | Inter-segment Sales
Business Segment Information
Net sales	7.3	2.3	12.5	4.9
Parts Supply | Total Sales
Business Segment Information
Net sales	278.0	244.6	806.6	711.6
Repair & Engineering
Business Segment Information
Net sales	215.9	140.8	662.3	423.7
Repair & Engineering | Inter-segment Sales
Business Segment Information
Net sales	20.5	23.6	64.3	65.2
Repair & Engineering | Total Sales
Business Segment Information
Net sales	236.4	164.4	726.6	488.9
Integrated Solutions
Business Segment Information
Net sales	162.9	165.5	495.2	478.4
Integrated Solutions | Inter-segment Sales
Business Segment Information
Net sales	0.5	0.2	1.1	0.6
Integrated Solutions | Total Sales
Business Segment Information
Net sales	163.4	165.7	496.3	479.0
Expeditionary Services
Business Segment Information
Net sales	28.7	18.7	74.4	53.6
Expeditionary Services | Total Sales
Business Segment Information
Net sales	$ 28.7	$ 18.7	$ 74.4	$ 53.6