Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 28, 2022	Feb. 28, 2021	Feb. 28, 2022	Feb. 28, 2021
Disaggregation of revenue by major customer markets
Net sales	$ 452.2	$ 410.3	$ 1,343.9	$ 1,214.7
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	438.0	389.7	1,292.9	1,138.3
Aviation Services | North America
Disaggregation of revenue by major customer markets
Net sales	324.2	318.2	1,013.0	927.1
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	50.1	49.0	162.5	145.7
Aviation Services | Other
Disaggregation of revenue by major customer markets
Net sales	63.7	22.5	117.4	65.5
Aviation Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	264.0	204.7	788.2	566.5
Aviation Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	174.0	185.0	504.7	571.8
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	14.2	20.6	51.0	76.4
Expeditionary Services | North America
Disaggregation of revenue by major customer markets
Net sales	14.2	20.3	50.8	73.6
Expeditionary Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	0.0	0.2	0.2	2.6
Expeditionary Services | Other
Disaggregation of revenue by major customer markets
Net sales	0.0	0.1	0.0	0.2
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	1.0	3.1	1.8	10.8
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	$ 13.2	$ 17.5	$ 49.2	$ 65.6