Business Segment Information - Geographic Data (Details) - USD ($) $ in Millions	12 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2020
Business Segment Information
Net sales	$ 1,820.0	$ 1,652.3	$ 2,072.0
Long-lived assets	566.7	602.7
United States
Business Segment Information
Long-lived assets	400.4	419.1
Europe
Business Segment Information
Long-lived assets	74.3	83.1
Other,
Business Segment Information
Long-lived assets	92.0	100.5
Foreign countries
Business Segment Information
Net sales	$ 484.5	$ 370.5	$ 591.8
Foreign countries | Total sales | Geographic concentration
Business Segment Information
Percentage of total sales	26.60%	22.40%	28.60%
Aviation Services
Business Segment Information
Net sales	$ 1,745.8	$ 1,553.7	$ 1,964.2
Aviation Services | North America
Business Segment Information
Net sales	1,346.2	1,255.7	1,505.6
Aviation Services | Europe
Business Segment Information
Net sales	223.7	207.5	330.8
Aviation Services | Other.
Business Segment Information
Net sales	175.9	90.5	127.8
Expeditionary Services
Business Segment Information
Net sales	74.2	98.6	107.8
Expeditionary Services | North America
Business Segment Information
Net sales	74.0	95.9	98.4
Expeditionary Services | Europe
Business Segment Information
Net sales	$ 0.2	2.6	9.0
Expeditionary Services | Other.
Business Segment Information
Net sales		$ 0.1	$ 0.4