Revenue recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Nov. 30, 2022	Nov. 30, 2021	Nov. 30, 2022	Nov. 30, 2021
Disaggregation of revenue by major customer markets
Net sales	$ 469.8	$ 436.6	$ 916.1	$ 891.7
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	445.7	419.3	869.7	854.9
Aviation Services | North America
Disaggregation of revenue by major customer markets
Net sales	353.7	341.2	677.0	688.8
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	51.9	50.4	114.3	112.4
Aviation Services | Other.
Disaggregation of revenue by major customer markets
Net sales	40.1	27.7	78.4	53.7
Aviation Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	309.9	257.0	602.0	524.2
Aviation Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	135.8	162.3	267.7	330.7
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	24.1	17.3	46.4	36.8
Expeditionary Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	23.5	17.3	45.4	36.6
Expeditionary Services | Other.
Disaggregation of revenue by major customer markets
Net sales	0.6		1.0	0.2
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	1.9	0.7	3.4	0.8
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	$ 22.2	$ 16.6	$ 43.0	$ 36.0