Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 29, 2024	Feb. 28, 2023	Feb. 29, 2024	Feb. 28, 2023
Disaggregation of revenue by major customer markets
Net sales	$ 567.3	$ 521.1	$ 1,662.4	$ 1,437.2
Parts Supply
Disaggregation of revenue by major customer markets
Net sales	242.3	227.6	706.7	579.8
Parts Supply | Commercial
Disaggregation of revenue by major customer markets
Net sales	200.2	179.7	595.6	451.0
Parts Supply | Government and defense
Disaggregation of revenue by major customer markets
Net sales	42.1	47.9	111.1	128.8
Repair & Engineering
Disaggregation of revenue by major customer markets
Net sales	140.8	128.0	423.7	390.4
Repair & Engineering | Commercial
Disaggregation of revenue by major customer markets
Net sales	128.2	114.0	380.7	348.8
Repair & Engineering | Government and defense
Disaggregation of revenue by major customer markets
Net sales	12.6	14.0	43.0	41.6
Integrated Solutions
Disaggregation of revenue by major customer markets
Net sales	165.5	143.5	478.4	398.6
Integrated Solutions | Commercial
Disaggregation of revenue by major customer markets
Net sales	69.1	44.7	195.3	140.6
Integrated Solutions | Government and defense
Disaggregation of revenue by major customer markets
Net sales	96.4	98.8	283.1	258.0
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	567.3	521.1	1,662.4	1,437.2
Aviation Services | U.S./Canada
Disaggregation of revenue by major customer markets
Net sales	422.2	385.8	1,236.5	1,108.2
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	90.4	71.0	263.6	186.3
Aviation Services | Asia/South Pacific
Disaggregation of revenue by major customer markets
Net sales	47.5	34.8	133.6	98.2
Aviation Services | Other
Disaggregation of revenue by major customer markets
Net sales	7.2	29.5	28.7	44.5
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	18.7	22.0	53.6	68.4
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	1.7	1.1	5.3	4.5
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	$ 17.0	$ 20.9	$ 48.3	$ 63.9