Description of Business, Basis of Presentation, and Significant Accounting Policies (Schedule of Recast of Selected Consolidated Statement of Cash Flow) (Details) - USD ($) $ in Millions		3 Months Ended												12 Months Ended
		May 31, 2019	Feb. 28, 2019	Nov. 30, 2018	Aug. 31, 2018	May 31, 2018		Feb. 28, 2018	[1]	Nov. 30, 2017	[1]	Aug. 31, 2017		May 31, 2019	May 31, 2018		May 31, 2017
Cash flows from operating activities
Net income		$ 230.4	$ 324.6	$ 235.8	$ 243.6	$ 217.7	[1]	$ 367.2		$ 198.8		$ 210.4	[1]	$ 1,034.4	$ 994.1	[1],[2],[3]	$ 826.3	[2],[3],[4]
Amortization of deferred contract costs														180.2	174.7	[3],[5]	169.4	[3],[5]
Provision/(benefit) for deferred income taxes														4.7	(37.2)	[3],[6]	22.7	[3],[6]
Accounts receivable and PEO unbilled receivables, net														(117.2)	16.2	[3],[5]	(103.3)	[3],[5]
Prepaid expenses and other current assets														1.0	18.0	[3],[5]	(32.2)	[3],[5]
Accounts payable and other current liabilities														77.5	42.9	[3],[5]	38.2	[3],[5]
Deferred costs														(188.5)	(181.8)	[3],[5]	(185.6)	[3],[5]
Net change in other long-term assets and liabilities														(5.4)	(5.7)	[3],[5]	(14.9)	[3],[5]
Cash flows from investing activities
Net cash (used in)/provided by investing activities														(1,628.3)	998.5	[3],[5]	(662.2)	[3],[5]
Net change in cash, cash equivalents, restricted cash and restricted cash equivalents														(1,365.3)	1,851.1	[3],[5]	(184.5)	[3],[5]
Cash, cash equivalents, restricted cash and restricted cash equivalents, beginning of fiscal year	[3],[5]				2,300.5							449.4		2,300.5	449.4		633.9
Cash, cash equivalents, restricted cash and restricted cash equivalents, end of fiscal year		$ 935.2				2,300.5	[3],[5]							935.2	2,300.5	[3],[5]	449.4	[3],[5]
As Previously Reported [Member]
Cash flows from operating activities
Net income															933.7		817.3
Provision/(benefit) for deferred income taxes															19.2		17.4
Accounts receivable and PEO unbilled receivables, net															13.6		(103.7)
Prepaid expenses and other current assets															17.7		(34.1)
Accounts payable and other current liabilities															42.6		39.1
Net change in other long-term assets and liabilities															(5.6)		(15.4)
Cash flows from investing activities
Net change in funds held for clients’ money market securities and other cash equivalents															(1,677.5)		237.6
Net cash (used in)/provided by investing activities															(679.0)		(424.6)
Net change in cash, cash equivalents, restricted cash and restricted cash equivalents															173.6		53.1
Cash, cash equivalents, restricted cash and restricted cash equivalents, beginning of fiscal year					358.2							184.6		358.2	184.6		131.5
Cash, cash equivalents, restricted cash and restricted cash equivalents, end of fiscal year						358.2									358.2		184.6
ASU 2014-09 [Member] | Adjustments [Member]
Cash flows from operating activities
Net income															60.4		9.0
Amortization of deferred contract costs															174.7		169.4
Provision/(benefit) for deferred income taxes															(56.4)		5.3
Accounts receivable and PEO unbilled receivables, net															2.6		0.4
Prepaid expenses and other current assets															0.3		1.9
Accounts payable and other current liabilities															0.3		(0.9)
Deferred costs															(181.8)		(185.6)
Net change in other long-term assets and liabilities															(0.1)		0.5
ASU 2016-18 [Member] | Adjustments [Member]
Cash flows from investing activities
Net change in funds held for clients’ money market securities and other cash equivalents															1,677.5		(237.6)
Net cash (used in)/provided by investing activities															1,677.5		(237.6)
Net change in cash, cash equivalents, restricted cash and restricted cash equivalents															1,677.5		(237.6)
Cash, cash equivalents, restricted cash and restricted cash equivalents, beginning of fiscal year					$ 1,942.3							$ 264.8		$ 1,942.3	264.8		502.4
Cash, cash equivalents, restricted cash and restricted cash equivalents, end of fiscal year						$ 1,942.3									$ 1,942.3		$ 264.8

[1] Amounts have been adjusted to reflect the adoption of ASC Topic 606.

[2] Amounts have been adjusted to reflect the adoption of Accounting Standards Codification ("ASC") Topic 606, "Revenue from Contracts with Customers" ("ASC Topic 606").

[3] Amounts have been adjusted to reflect the adoption of Accounting Standards Update ("ASU") No. 2016-18, "Statement of Cash Flows (Topic 230): Restricted Cash (a consensus of the FASB Emerging Issues Task Force)."

[4] Amounts have been adjusted to reflect the adoption of ASC Topic 606.

[5] Amounts have been adjusted to reflect the adoption of ASC Topic 606.

[6] Amounts have been adjusted to reflect the adoption of ASC Topic 606.