Five boroughs standard quotas for city council seats are given as follows. Use Webster's method to round the quota given for the Bronx.

Manhattan: 10.67
The Bronx: 5.99
Queens: 11.51
Brooklyn: 11.01
Staten Island: 1.59

Step 1 ：Given the quotas for the five boroughs are as follows: Manhattan: 10.67, The Bronx: 5.99, Queens: 11.51, Brooklyn: 11.01, Staten Island: 1.59.

Step 2 ：We are asked to round the quota for The Bronx using Webster's method.

Step 3 ：Webster's method is a method for apportionment, which is the process of rounding numbers to the nearest whole number.

Step 4 ：In this case, we need to round the quota given for The Bronx, which is 5.99.

Step 5 ：Using Webster's method, we round 5.99 to the nearest whole number.

Step 6 ：The rounded quota for The Bronx is 6.

Step 7 ：Final Answer: The rounded quota for The Bronx using Webster's method is \(\boxed{6}\).