SQL Cast as Date

Hi Experts,

I am working with an old MS SQL database where the date is stored as Varchar, but I keep getting the following error

Msg 241, Level 16, State 1, Line 1
Conversion failed when converting date and/or time from character string.

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You will see that I am trying two formats, both unsuccessfull

SELECT SUM(family) AS totFam, SUM(adults) AS totAdult, SUM(Seniors) AS totSen, SUM(students) AS totStud, 
SUM(children) AS totChild, SUM(infants) AS totInf 
FROM Invoices 

WHERE CAST( CASE WHEN responseCode IS NULL OR ISNUMERIC(ResponseCode) = 0 THEN '99' else responsecode end AS INT) < 50 
AND (Company = 'CSST' OR Company = 'COMBO') 

/*AND CAST(paymentDate AS DATE) >= CAST('12/5/2019' AS DATE) AND CAST(paymentDate AS DATE) <= CAST('3/24/2020' AS DATE)*/
AND CAST(paymentDate AS DATE) >= CAST('2019-12-05' AS DATE) AND CAST(paymentDate AS DATE) <= CAST('2020-03-24' AS DATE)

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When I do a simple SELECT ..... ,CAST(paymentDate AS DATE) AS dt I get YYYY-MM-DD

Thank you,