Disclaimer: I grew up speaking Turkish, but never studied it. I think I can give a common-sense explanation, but can’t give a rigorous “proof” appealing to grammatical rules.

I read “(5’le 3’ün farkını) yaz” as “having 5, 3’s difference write” (of course this is not natural in English). Ie, you’re given 5, you want to take 3, and write the result. Likewise, “(3’ün 5’le farkını) yaz” would be “3’s difference, having 5, write”. Again we are given 5, and want 3’s difference. Because we’re starting with 5, i think there is no ambiguity in the operation to be done — start with 5, subtract 3.

Idk if that actually helps clarify it at all, maybe it gives some intuition