Maybe there are other ways to deal with this, but a standard procedure with the fifth way is to argue against platonism, so that some sort of divine conceptualism becomes the only or best possible option.

1- To be fair, we should them take the objections to the same standards of not requiring advanced metaphysics foundations then. But most people will find platonism a rather strange view, to say nothing of its problems. By comparison, explaining order and final causes in terms of intelligence -- a divine intelligence, in this case -- is much more closer to our own experience, and certainly seems more sensible. (Hume can bite me). From experience, we know that intelligence is an explanation for order. When we see a bookshelf in which the books are alphabetically arranged, we rightly assume that a person has arranged them. Although the analogy is imprecise to the point where order in the bookshelf is something extrinsic, and we're looking for an explanation for intrinsic order with the fifth way, my point is that we are much more familiar with the fact that minds cause order, and therefore to conclude a divine mind to explain order in the cosmos seems much more plausible and intuitive than platonism.

2- Norris Clarke defends a teleological argument in "The One and the Many" in which he stresses the fact that our universe is a dynamic system in which elements are ordered to interact with one another in stable relationships (which we then call laws). In such systems, the nature of each element is defined by its relation to others; the relation to the whole affects all the parts. We then need an explanation of the unity of the system as a whole, and no part can do that by itself, since it presupposes the others already related to it before it can have its action. He then argues that a cause of this order can only be one possessing intelligence, because only an idea or set of ideas can correlate and unify many different beings into such a dynamic, cooperative order whilst also "leaving their distinct beings intact".

Clarke doesn't mention platonism, perhaps because he already takes it as metaphysically problematic, but maybe because he also thinks it is not capable of explaining what has just been described?. That is my view, at least. I think this argument points to something in teleology that can only be explained by some sort of intelligente (in this case, divine intelligence); I don't think it could be possible for platonic forms to explain the cooperative and unitary order among all their different instantiations, since they'd already presuppose each other related to one another so as to explain their action. But then positing this unitary cooperative order as a standalone form doesn't seem to make sense, because such an order is, in a way, dependent on its parts to exist. It seems like platonism gets caught up in a vicious circle. But a mind -- which by itself is not dependent on the forms to exist -- can actually draw all distinct forms into a cooperative order; causing a unitary harmonic whole whilst being itself (the mind) independent of the forms, and simultaneously respecting their distinct beings.

So classic teleology may indeed be only explainable by a divine mind, irrespective of all other problems platonism faces.