Revenue recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 28, 2019	Feb. 28, 2018	Feb. 28, 2019	Feb. 28, 2018
Disaggregation of Revenue
Sales	$ 529.5	$ 456.3	$ 1,489.1	$ 1,274.8
Aviation Services
Disaggregation of Revenue
Sales	497.3	429.0	1,398.6	1,192.0
Aviation Services | North America
Disaggregation of Revenue
Sales	373.7	285.8	1,024.9	811.3
Aviation Services | Europe/Africa
Disaggregation of Revenue
Sales	80.9	87.1	245.4	242.3
Aviation Services | Other
Disaggregation of Revenue
Sales	42.7	56.1	128.3	138.4
Aviation Services | Commercial
Disaggregation of Revenue
Sales	350.8	340.2	983.0	940.4
Aviation Services | Government and defense
Disaggregation of Revenue
Sales	146.5	88.8	415.6	251.6
Expeditionary Services
Disaggregation of Revenue
Sales	32.2	27.3	90.5	82.8
Expeditionary Services | North America
Disaggregation of Revenue
Sales	30.2	19.7	85.1	71.4
Expeditionary Services | Europe/Africa
Disaggregation of Revenue
Sales	1.5	7.4	4.2	11.1
Expeditionary Services | Other
Disaggregation of Revenue
Sales	0.5	0.2	1.2	0.3
Expeditionary Services | Commercial
Disaggregation of Revenue
Sales	6.8	11.0	23.3	28.5
Expeditionary Services | Government and defense
Disaggregation of Revenue
Sales	$ 25.4	$ 16.3	$ 67.2	$ 54.3