Test Data
DECLARE @TABLE TABLE (Dates VARCHAR(20))
INSERT INTO @TABLE VALUES 
('10/05/2015'),
('11/05/2015'),
('1/5/2015'),
('01/5/2014')
Query
The following query will convert all the values to proper sql server date data type.
SELECT CONVERT(DATE,
       RIGHT('0000' + PARSENAME(REPLACE(Dates , '/','.'),1),4)
     + RIGHT('00'   + PARSENAME(REPLACE(Dates , '/','.'),2),2)
     + RIGHT('00'   + PARSENAME(REPLACE(Dates , '/','.'),3),2)
      )
FROM @TABLE
Result
2015-05-10
2015-05-11
2015-05-01
2014-05-01
Once you have got the values in well-formatted sql server date type, you can extend the query to get the required output yyyy/mm/dd by doing the following:
SELECT  CONVERT(VARCHAR(10), 
      CONVERT(DATE,
       RIGHT('0000' + PARSENAME(REPLACE(Dates , '/','.'),1),4)
     + RIGHT('00'   + PARSENAME(REPLACE(Dates , '/','.'),2),2)
     + RIGHT('00'   + PARSENAME(REPLACE(Dates , '/','.'),3),2)
      ), 111)
FROM @TABLE
Result
2015/05/10
2015/05/11
2015/05/01
2014/05/01