Quarterly report pursuant to Section 13 or 15(d)

Description of Business, Basis of Presentation, and Significant Accounting Policies (Schedule of Recast of Selected Unaudited Consolidated Statement of Cash Flow) (Details)

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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)."