Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Nov. 30, 2023	Nov. 30, 2022	Nov. 30, 2023	Nov. 30, 2022
Disaggregation of revenue by major customer markets
Net sales	$ 545.4	$ 469.8	$ 1,095.1	$ 916.1
Parts Supply
Disaggregation of revenue by major customer markets
Net sales	227.6	183.6	464.4	352.2
Parts Supply | Commercial
Disaggregation of revenue by major customer markets
Net sales	189.4	141.5	395.4	271.3
Parts Supply | Government and defense
Disaggregation of revenue by major customer markets
Net sales	38.2	42.1	69.0	80.9
Repair & Engineering
Disaggregation of revenue by major customer markets
Net sales	145.4	134.8	282.9	262.4
Repair & Engineering | Commercial
Disaggregation of revenue by major customer markets
Net sales	130.9	122.1	252.5	234.8
Repair & Engineering | Government and defense
Disaggregation of revenue by major customer markets
Net sales	14.5	12.7	30.4	27.6
Integrated Solutions
Disaggregation of revenue by major customer markets
Net sales	156.6	127.3	312.9	255.1
Integrated Solutions | Commercial
Disaggregation of revenue by major customer markets
Net sales	63.4	46.3	126.2	95.9
Integrated Solutions | Government and defense
Disaggregation of revenue by major customer markets
Net sales	93.2	81.0	186.7	159.2
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	545.4	469.8	1,095.1	916.1
Aviation Services | U.S./Canada
Disaggregation of revenue by major customer markets
Net sales	405.4	377.2	814.3	722.4
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	81.8	52.5	173.2	115.3
Aviation Services | Asia/South Pacific
Disaggregation of revenue by major customer markets
Net sales	44.9	32.4	86.1	63.4
Aviation Services | Other
Disaggregation of revenue by major customer markets
Net sales	13.3	7.7	21.5	15.0
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	15.8	24.1	34.9	46.4
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	1.5	1.9	3.6	3.4
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	$ 14.3	$ 22.2	$ 31.3	$ 43.0