Database VIEW with a dynamically changing filter
You can't do what you want with a view.  You have to use a function.  Note that I didn't retain all your double quoting of identifiers, so you will have to put them back if you insist.

CREATE OR REPLACE FUNCTION public.calls_view(timestamp with time zone, timestamp with time zone)
 RETURNS SETOF calls
 LANGUAGE sql
AS $function$
SELECT *
FROM Calls
WHERE CustomerName IN (SELECT CustomerName
                         FROM Calls
                         WHERE Quality='Bad' and timestamp between $1 and $2
                         GROUP BY CustomerName
                         ORDER BY COUNT(*) DESC LIMIT 5)
  AND Quality='Bad' and timestamp between $1 and $2 
$function$


You can use it kind of like a view, but you must supply your parameters in parentheses, not a WHERE clause:

select * from calls_view(now() - interval '1 day', now());