Business Segment Information - Geographic Data (Details) - USD ($) $ in Millions	12 Months Ended
	May 31, 2024	May 31, 2023	May 31, 2022
Business Segment Information
Net sales	$ 2,318.9	$ 1,990.5	$ 1,820.0
Long-lived assets	1,380.4	735.2
United States
Business Segment Information
Long-lived assets	1,174.6	559.9
Europe/Africa
Business Segment Information
Long-lived assets	90.9	78.5
Other
Business Segment Information
Long-lived assets	114.9	96.8
Foreign countries
Business Segment Information
Net sales	$ 770.0	$ 588.6	$ 484.5
Foreign countries | Total sales | Geographic concentration
Business Segment Information
Percentage of total sales	33.20%	29.60%	26.60%
Parts Supply
Business Segment Information
Net sales	$ 967.0	$ 818.4	$ 678.3
Parts Supply | North America
Business Segment Information
Net sales	532.1	493.3	414.0
Parts Supply | Europe/Africa
Business Segment Information
Net sales	252.9	190.8	144.9
Parts Supply | Asia
Business Segment Information
Net sales	146.4	108.9	88.0
Parts Supply | Other
Business Segment Information
Net sales	35.6	25.4	31.4
Repair & Engineering
Business Segment Information
Net sales	640.1	533.4	470.7
Repair & Engineering | North America
Business Segment Information
Net sales	572.1	488.6	438.7
Repair & Engineering | Europe/Africa
Business Segment Information
Net sales	40.6	25.2	20.6
Repair & Engineering | Other
Business Segment Information
Net sales	27.4	19.6	11.4
Integrated Solutions
Business Segment Information
Net sales	641.9	546.9	596.8
Integrated Solutions | North America
Business Segment Information
Net sales	536.0	461.7	493.5
Integrated Solutions | Europe/Africa
Business Segment Information
Net sales	78.0	51.4	58.2
Integrated Solutions | Other
Business Segment Information
Net sales	27.9	33.8	45.1
Expeditionary Services
Business Segment Information
Net sales	69.9	91.8	74.2
Expeditionary Services | North America
Business Segment Information
Net sales	68.6	89.6	74.0
Expeditionary Services | Other
Business Segment Information
Net sales	$ 1.3	$ 2.2	$ 0.2