Business Segment Information - Sales and Gross Profit (Details) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 28, 2022 USD ($)	Feb. 28, 2021 USD ($)	Feb. 28, 2022 USD ($) segment	Feb. 28, 2021 USD ($)
Disaggregation of revenue by major customer markets
Operating segments (in segments) | segment			2
Sales	$ 452.2	$ 410.3	$ 1,343.9	$ 1,214.7
Gross profit	80.4	86.0	223.4	204.1
Aviation Services
Disaggregation of revenue by major customer markets
Sales	438.0	389.7	1,292.9	1,138.3
Gross profit	77.9	82.5	212.8	193.9
Expeditionary Services
Disaggregation of revenue by major customer markets
Sales	14.2	20.6	51.0	76.4
Gross profit	$ 2.5	$ 3.5	$ 10.6	$ 10.2