Business Segment Information - Sales by Segment (Details) $ in Millions	3 Months Ended
	Aug. 31, 2023 USD ($) segment	Aug. 31, 2022 USD ($)
Business Segment Information
Number of new operating segments | segment	3
Net sales	$ 549.7	$ 446.3
Inter-segment Sales
Business Segment Information
Net sales	21.4	22.1
Third-Party Sales
Business Segment Information
Net sales	571.1	468.4
Parts Supply
Business Segment Information
Net sales	236.8	168.6
Parts Supply | Inter-segment Sales
Business Segment Information
Net sales	0.8	1.8
Parts Supply | Third-Party Sales
Business Segment Information
Net sales	237.6	170.4
Repair & Engineering
Business Segment Information
Net sales	137.5	127.6
Repair & Engineering | Inter-segment Sales
Business Segment Information
Net sales	19.5	20.3
Repair & Engineering | Third-Party Sales
Business Segment Information
Net sales	157.0	147.9
Integrated Solutions
Business Segment Information
Net sales	156.3	127.8
Integrated Solutions | Inter-segment Sales
Business Segment Information
Net sales	1.1
Integrated Solutions | Third-Party Sales
Business Segment Information
Net sales	157.4	127.8
Expeditionary Services
Business Segment Information
Net sales	19.1	22.3
Expeditionary Services | Third-Party Sales
Business Segment Information
Net sales	$ 19.1	$ 22.3