Revenue recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Nov. 30, 2021	Nov. 30, 2020	Nov. 30, 2021	Nov. 30, 2020
Disaggregation of revenue by major customer markets
Net sales	$ 436.6	$ 403.6	$ 891.7	$ 804.4
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	419.3	385.0	854.9	748.6
Aviation Services | North America
Disaggregation of revenue by major customer markets
Net sales	341.2	314.1	688.8	608.9
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	50.4	45.7	112.4	96.7
Aviation Services | Other
Disaggregation of revenue by major customer markets
Net sales	27.7	25.2	53.7	43.0
Aviation Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	257.0	192.2	524.2	361.8
Aviation Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	162.3	192.8	330.7	386.8
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	17.3	18.6	36.8	55.8
Expeditionary Services | North America
Disaggregation of revenue by major customer markets
Net sales	17.3	18.4	36.6	53.3
Expeditionary Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	0.0	0.2	0.2	2.4
Expeditionary Services | Other
Disaggregation of revenue by major customer markets
Net sales	0.0	0.0	0.0	0.1
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	0.7	2.0	0.8	7.7
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	$ 16.6	$ 16.6	$ 36.0	$ 48.1