Revenue recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended
	Aug. 31, 2023	Aug. 31, 2022
Disaggregation of revenue by major customer markets
Net sales	$ 549.7	$ 446.3
U.S./Canada
Disaggregation of revenue by major customer markets
Net sales	408.9	345.2
Parts Supply
Disaggregation of revenue by major customer markets
Net sales	236.8	168.6
Parts Supply | Commercial
Disaggregation of revenue by major customer markets
Net sales	206.0	129.8
Parts Supply | Government and defense
Disaggregation of revenue by major customer markets
Net sales	30.8	38.8
Repair & Engineering
Disaggregation of revenue by major customer markets
Net sales	137.5	127.6
Repair & Engineering | Commercial
Disaggregation of revenue by major customer markets
Net sales	121.6	112.7
Repair & Engineering | Government and defense
Disaggregation of revenue by major customer markets
Net sales	15.9	14.9
Integrated Solutions
Disaggregation of revenue by major customer markets
Net sales	156.3	127.8
Integrated Solutions | Commercial
Disaggregation of revenue by major customer markets
Net sales	62.8	49.6
Integrated Solutions | Government and defense
Disaggregation of revenue by major customer markets
Net sales	93.5	78.2
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	549.7	446.3
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	91.4	62.8
Aviation Services | Asia/South Pacific
Disaggregation of revenue by major customer markets
Net sales	41.2	31.0
Aviation Services | Other
Disaggregation of revenue by major customer markets
Net sales	8.2	7.3
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	19.1	22.3
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	2.1	1.5
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	$ 17.0	$ 20.8