Some people enjoy Aquinas, while others find him hard to read. If you don't want to read the original, or just want to read the same five ways, explained in more modern terms, I suggest Msgr. Ronald Knox. This is from Chapter 4 of Belief of Catholics:
- In all motion, or rather, as we should say, in all change, you can separate two elements, active and passive, that which is changed and that which changes it. But, in our experience, the agent in such change is not self-determined, but determined in its turn by some higher agent. Can this process go on ad infinitum? No, for an infinite series of agents, none of them self-determined, would not give us the finality which thought demands; there must be, at the beginning of the series, however long, an Agent who is self-determined, who is the ultimate Agent in the whole cycle of changes that proceeds from him.
- Similarly, in our experience every event is determined by a cause. But that cause in its turn is itself an event determined by a cause. An infinite series of causes would give no explanation of how the causation ever began. There must therefore be an uncaused Cause, which is the ultimate Cause of the whole nexus of events which proceeds from it.
- In our experience, we find nothing which exists in its own right; everything depends for its existence on something else. This is plain in the case of the organised individual; for plants, animals, etc., are born, live, and die; that is to say, their existence is only contingent, not necessary-- it depends on conditions outside itself. Now, although the whole sum of matter does not, in our experience, increase or diminish, we cannot think of it as existing necessarily-- it is just there. Its existence, then, must depend on something outside itself--something which exists necessarily, of its own right. That Something we call God.
- In our experience, there are various degrees of natural perfection. But the existence of the good and the better implies the existence of a Best; for (according to Plato's system of thought) this Best is itself the cause and the explanation of all good. But this Best is not found in our earthly experience, therefore it must lie beyond our earthly experience; and it is this Best which we call God.
- Everywhere in Nature we observe the effects of order and system. If blind chance ruled everything, this prevalence of order would be inexplicable; it would be a stupendous coincidence. Order can only be conceived as the expression of a Mind; and, though our mind appreciates the existence of order in the world, it is not our mind which has introduced it there. There must therefore exist outside our experience, a Mind of which this order is the expression; and that Mind we call God.
Understand these five arguments, and what they prove, and you're well on the way to making the intellectual case for God.
It is often objected that this analysis of the facts is unnecessarily itemised; it repeats the same argument under different forms. For the purposes of the plain man, it may perhaps be admitted that the first three of these arguments are not readily distinguishable. He apprehends God in his Creation, first as all-powerful and the source of all power (i., ii., and iii.); then as all-good and the source of all goodness (iv.); then as all-wise and the source of all wisdom (v.). For all the changes that have swept over Europe since the twelfth century, he has not been bullied out of his conviction.