Description of Business, Basis of Presentation, and Significant Accounting Policies (Schedule of Recast of Selected Unaudited Consolidated Statement of Cash Flow) (Details) - USD ($) $ in Millions		3 Months Ended						6 Months Ended		9 Months Ended
		Feb. 28, 2019		Aug. 31, 2018		Feb. 28, 2018		Nov. 30, 2018		Feb. 28, 2019		Feb. 28, 2018		May 31, 2018	[1]
Cash flows from operating activities
Net income		$ 324.6				$ 367.2	[1],[2]			$ 804.0	[3]	$ 776.4	[1],[2],[3]
Amortization of deferred contract costs	[3]									134.8		130.5	[1]
Provision/(benefit) for deferred income taxes	[3]									10.7		(45.0)	[1]
Accounts receivable	[3]									(110.2)		(27.8)	[1]
Accounts payable and other current liabilities	[3]									108.4		81.4	[1]
Deferred costs	[3]									(134.1)		(128.5)	[1]
Net change in other long-term assets and liabilities	[3]									(8.0)		2.8	[1]
Cash flows from investing activities
Net cash provided by investing activities				$ 156.0				$ 53.7		(538.6)	[3]	433.5	[1],[3]
Increase/(decrease) in cash, cash equivalents, restricted cash and restricted cash equivalents				(680.6)				(832.7)		1,405.0	[3]	548.4	[1],[3]
Cash, cash equivalents, restricted cash and restricted cash equivalents, beginning of fiscal year		1,467.8		2,300.5	[3]			2,300.5	[3]	2,300.5	[3]	449.4	[1],[3]
Cash, cash equivalents, restricted cash and restricted cash equivalents, end of period		3,705.5	[3]	1,619.9		997.8	[1],[3]	1,467.8		3,705.5	[3]	997.8	[1],[3]
Reconciliation of cash, cash equivalents, restricted cash and restricted cash equivalents to the Consolidated Balance Sheets
Cash and cash equivalents		696.4	[3]	440.1		323.9	[1],[3]	510.6		696.4	[3]	323.9	[1],[3]	$ 358.2
Restricted cash and restricted cash equivalents included in funds held for clients		2,874.7	[3]	1,179.8		673.9	[1],[3]	957.2		2,874.7	[3]	673.9	[1],[3]
As Previously Reported [Member]
Cash flows from operating activities
Net income												705.2
Provision/(benefit) for deferred income taxes												6.5
Accounts receivable												(6.2)
Accounts payable and other current liabilities												80.9
Deferred costs
Net change in other long-term assets and liabilities												3.4
Cash flows from investing activities
Net change in funds held for clients’ money market securities and other cash equivalents				762.5				985.1				(409.1)
Net cash provided by investing activities				918.5				1,038.8				24.4
Increase/(decrease) in cash, cash equivalents, restricted cash and restricted cash equivalents				81.9				152.4				139.3
Cash, cash equivalents, restricted cash and restricted cash equivalents, beginning of fiscal year		510.6		358.2				358.2		358.2		184.6
Cash, cash equivalents, restricted cash and restricted cash equivalents, end of period				440.1		323.9		510.6				323.9
Adjustments [Member]
Cash flows from investing activities
Net change in funds held for clients’ money market securities and other cash equivalents				(762.5)				(985.1)
Net cash provided by investing activities				(762.5)				(985.1)
Increase/(decrease) in cash, cash equivalents, restricted cash and restricted cash equivalents				(762.5)				(985.1)
Cash, cash equivalents, restricted cash and restricted cash equivalents, beginning of fiscal year		$ 957.2		1,942.3				1,942.3		$ 1,942.3
Cash, cash equivalents, restricted cash and restricted cash equivalents, end of period				$ 1,179.8				$ 957.2
ASU 2014-09 [Member] | As Previously Reported [Member]
Cash flows from operating activities
Net income						260.4						705.2
ASU 2014-09 [Member] | Adjustments [Member]
Cash flows from operating activities
Net income						106.8						71.2
Amortization of deferred contract costs												130.5
Provision/(benefit) for deferred income taxes												(51.5)
Accounts receivable												(21.6)
Accounts payable and other current liabilities												0.5
Deferred costs												(128.5)
Net change in other long-term assets and liabilities												(0.6)
ASU 2016-18 [Member] | Adjustments [Member]
Cash flows from operating activities
Deferred costs
Cash flows from investing activities
Net change in funds held for clients’ money market securities and other cash equivalents												409.1
Net cash provided by investing activities												409.1
Increase/(decrease) in cash, cash equivalents, restricted cash and restricted cash equivalents												409.1
Cash, cash equivalents, restricted cash and restricted cash equivalents, beginning of fiscal year												264.8
Cash, cash equivalents, restricted cash and restricted cash equivalents, end of period						$ 673.9						$ 673.9

[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)."