This essay will argue that Aquinas' 5th way is ultimately unconvincing. It can be defended against Hume's critique. However, even the modern improvement of Aquinas' 5th way by Swinburne cannot be defended against alternate scientific possibilities like the multiverse.
Aquinas' 5th way is an a posteriori argument, based on the observation of the behaviour of objects in the universe. It is an inductive argument, meaning the truth of
the premises are supposed to provide evidence in favour of the conclusion of God's
existence. Aquinas observed that things we observe in the universe are goal-
directed - they don't behave randomly. E.g. flowers move towards the sun. Birds fly
south in winter. The water cycle. Things are not intelligent, or not intelligent enough,
to direct their own behaviour. This means there must be natural laws (laws of
nature/physics) which govern the behaviour of things in the universe. All beings -
living or not, have a nature which inclines their behaviour towards a certain goal
(telos). E.g. the birds have an 'instinct' put into them. Human nature is to know and
follow the primary precepts - that's the natural law in human nature. Natural laws
must have an origin. The only thing capable of creating natural laws would be an
intelligent designer. So, God exists. Analogy: Archer and the arrow - if you see an arrow, it's goal-directed towards a target; you can know there must be an archer that shot it, i.e. when we observe an unintelligent object behaving in a goaldirected way we can know there must be an intelligent mind who directed it towards that.

Similarly, when we observe in the universe goal-directed behaviour of objects which suggests there is a being which directed their behaviour through creating natural laws (God). Hume criticised teleological arguments like Aquinas' 5th way but pointing out that the Christian God is not the only explanation of design. If the design argument worked - it would not prove a particular God like the Christian God. It is just as likely that the universe was designed by a committee of Gods, polytheism, a junior God, or even a God who then died. And there is no basis for preferring the Christian God as an explanation of the design in the universe, compared to those other options Hume points out. So even if the design argument is logically sound, it has a very limited scope-it cannot be used to establish the truth of any specific religious belief.
Swinburne however counter's Hume and says that one God is simpler than many
Ockham's razor - we should go with the simplest explanation that works.
Swinburne accepts design argument can't prove Christian God in particular.
Aquinas and Paley also accept that. The problem for Hume is that they aren't trying to
prove the Christian God in particular. They are only trying to show that it is rational
and reasonable to believe in a God. All three theologians are following Aquinas
Natural theology, which involves logical inductive argument, intended to support faith rather than categorically prove the Christian God in particular). So the proponents of the design argument never claimed that it proved what Hume is accusing them of.

It looks like Hume did overreach with his argument in this case. The design
argument is limited in what it can prove, but Paley and Aquinas accepted that. They
never tried to show that Hume said they couldn't. The design argument still
seems to establish that there is at least some kind of God, which is a boost to faith,
at any rate to faith in some kind of God. To the extend that anyone does have faith in God,
then if there is evidence for at least some type of God, that still helps their faith, which is
all it was ever intended to do. It is something, at least.

Swinburne has the most modern variety of design argument - known as the 'fine tuning'
argument. It owes more to Aquinas' 5th way than Paley. Paley discussed the order of
things in space - such as the parts of the human eye. But this was refuted by
evolution. Aquinas discussed the order of object's behaviour over time due to natural
laws. Evolution can't actually account for the laws of physics themselves.
Swinburne develops this point, thinking that Aquinas was 'wiser' about this approach.
We know so much more about natural laws now. E.g. we know the charge of an
electron is. If these laws were all different and there was more or less charge - then atoms could
not exist - it spirals into or out of the nucleus - and we
couldn’t exist. It looks like the laws of physics must be exactly as they are - to
trillionth of degrees - in order for us to exist. So, Swinburne concludes that it’s more
reasonable to believe that a God intentionally designed the laws of physics to be
‘fine tuned’ for our existence - compared to believing that it was just by chance that
these laws exist.

Swinburne has most up-to-date form of design argument - known as 'fine tuning'
argument. Most similar to Aquinas' 5th way rather than Paley. Paley discussed the
order of things in space - for example, the parts of the human eye. However this
was disputed by evolution. Aquinas discussed the order of objects behaviour over
time due to natural laws. Evolution can't actually explain the laws of physics
themselves.
Swinburne extends this, saying that Aquinas was 'wiser' in his argument.
We now know a great deal more regarding natural laws. E.g. we know what the charge of an
electron is. If the laws were different and the electron had any more or less charge -
then atoms could not exist - it would spiral into or out of the nucleus - and we
couldn't exist. It seems the laws of physics can only be precisely as they are-to trillionth of degrees-for us to exist. So, Swinburne concludes that it is more reasonable to believe a God deliberately designed the laws of physics to be 'fine tuned' for our existence, rather than this being a chance occurrence.

Swinburne tried to say that there is no scientific evidence for the multiverse theory. But there doesn't have to be evidence of it in order to refute Swinburne's argument. All that has to be the case is that it could be true, in which case we are no longer forced to accept Swinburne's conclusion that a God is the only reasonable explanation of the laws of physics. Swinburne is making the same mistake as Paley: he identifies the area of scientific ignorance in his time and concludes that God must explain that. Just because science can't explain the laws of physics doesn't justify the thought that God must explain them. We should just side with Hume, who said we simply lack the evidence to know why the universe is the way it is. And because we cannot say that we know, it automatically disqualifies saying that this must have been God's doing, which was what the teleological argument was trying to prove.

Aquinas' 5th way can be defendable against superficial criticisms like those by Hume who didn't understand the approach of natural theology; however, more modern scientific concepts such as the multiverse really prove that reality is stranger and far more complicated than Aquinas managed to consider. The multiverse possibility explains every possible permutation of the universe we might observe but without God. Therefore, Aquinas' 5th way fails to show that belief in God is necessary in order to account for why the world is one way rather than another.