Yes, it would - and welcome to the forum!
The Walther Q5 comes with three mounting plates conforming to three different mounting norms, namely Trijicon, Leupold and Docter. Your Burris Fast Fire 3 should conform to the Docter mounting norm.
To avoid repeating what others have already posted, I'll refer you to some forum threads on the topic:
https://www.waltherforums.com/forum/ppq/56513-burris-fastfire3-ppq-q5-match.html
https://www.waltherforums.com/forum/ppq/58930-q5-match-red-dot-options.html
Note that you might have to look around a bit to find the correct screws.
Balor
