Revenue from Contracts with Customers - Revenue Disaggregated By Contract Type (Details) - USD ($) $ in Millions	3 Months Ended	9 Months Ended
Feb. 29, 2020	Mar. 02, 2019	Feb. 29, 2020	Mar. 02, 2019
Disaggregation of Revenue [Line Items]
Net sales	$ 665.7	$ 619.0	$ 2,010.8	$ 1,896.2
Single performance obligation \| Product revenue
Disaggregation of Revenue [Line Items]
Net sales	561.1	524.5	1,699.9	1,599.0
Multiple performance obligations \| Product revenue
Disaggregation of Revenue [Line Items]
Net sales	98.9	89.0	294.5	281.7
Multiple performance obligations \| Service revenue
Disaggregation of Revenue [Line Items]
Net sales	2.5	2.8	7.8	8.7
Other
Disaggregation of Revenue [Line Items]
Net sales	$ 3.2	$ 2.7	$ 8.6	$ 6.8

Amount, excluding tax collected from customer, of revenue from satisfaction of performance obligation by transferring promised good or service to customer. Tax collected from customer is tax assessed by governmental authority that is both imposed on and concurrent with specific revenue-producing transaction, including, but not limited to, sales, use, value added and excise.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 4
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=109196051&loc=SL49130543-203045

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 1
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=109196051&loc=SL49130539-203045

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 606
-SubTopic 10
-Section 50
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=109196051&loc=SL49130545-203045

Name:	us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration