i don't see anything in Romans 5 that would indicate that. but in Genesis 3 there is the cursing of the ground, and Satan cursed 'more than all cattle and more than every beast of the field' -- can surmise that the ground was not cursed before that, but what the LORD says to Satan here is amazing and extraordinarily difficult to understand; what do cattle & creatures of the fields have to do with any of what's recorded there? were they cursed beforehand? why? why doesn't the scripture mention anything about that? or are they cursed in conjunction with what is recorded here? is that all part of 'cursed is the ground for your sake' ?
it connects back to Romans 8; all creation was subject to futility, to 'the bondage of decay' not of its own will, and groans in earnest expectation for the adoption of the children of God. this passage seems to me to indicate Romans 5 isn't talking about 'only the death of animals, not men' -- as well as does the fact that, despite the interpretive choices having been made in our English translations, Genesis 1-2 calls creatures "living souls" exactly as it calls man a "living soul" -- it's the same phrase in Hebrew, but men decided to translate nephesh as 'creature' when He describes His creation of non-human living beings, and only 'soul' when He describes Adam. anthropocentric bias, anyone?
i'd have to hear the argument. i don't see it just from what i know/remember about the text -- tho it could, and i suspect it is, not an argument made from scripture at all, but an argument made from another logic and then shoehorned into interpretation of the text. that's not necessarily bad in and of itself - the Bible leaves details out of accounts all the time, and i think we are meant to think about these things and attempt to infer details as we meditate on what the things which are written for us mean about the things that are not written. but to wonder about the 'missing information' in the accounts in the Book is certainly an opportunity to get a lot of things very much wrong.