You cannot use window functions in a sentence Where(only in SELECTor ORDER BY).
But instead, you can use CTE :
WITH CTE
AS (SELECT fs.docu_id AS docID,
fs.field_3 AS ProductNo,
fs.field_4 AS [Status],
fs.field_5 AS [Index],
pd.[doku_nr] AS docIDshort,
Row_number() OVER(
Partition BY fs.field_3
ORDER BY fs.field_5 DESC) AS rownum
FROM [table1] fs
JOIN [table2] pd
ON fs.docu_id = pd.docu_id
AND fs.field_4 = 'valid')
SELECT docid, productno, status, [index], docIDshort
FROM CTE
WHERE rownum = 1