Revenue recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 28, 2023	Feb. 28, 2022	Feb. 28, 2023	Feb. 28, 2022
Disaggregation of revenue by major customer markets
Net sales	$ 521.1	$ 452.2	$ 1,437.2	$ 1,343.9
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	499.1	438.0	1,368.8	1,292.9
Aviation Services | North America
Disaggregation of revenue by major customer markets
Net sales	364.3	324.2	1,041.3	1,013.0
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	70.5	50.1	184.8	162.5
Aviation Services | Other
Disaggregation of revenue by major customer markets
Net sales	64.3	63.7	142.7	117.4
Aviation Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	338.4	264.0	940.4	788.2
Aviation Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	160.7	174.0	428.4	504.7
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	22.0	14.2	68.4	51.0
Expeditionary Services | North America
Disaggregation of revenue by major customer markets
Net sales	21.5	14.2	66.9	50.8
Expeditionary Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	0.5		1.5	0.2
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	1.1	1.0	4.5	1.8
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	$ 20.9	$ 13.2	$ 63.9	$ 49.2