Faith and Reason: How can we believe what we can't prove?

        Do faith and reason contradict each other?  How can you prove that God exists?
        It seems like the idea that God exists is self-evident, but how do you demonstrate it?
        Everyone has the knowledge of God, so it only makes sense that he exists.  It is kind of like the existence of truth; you can't prove that truth exists, but it's self-evident that it does.  Everyone understands that God is something which there is nothing greater than.  This proves that God exists mentally, but not actually.  It is hard to argue whether God exists actually.
        The existence of God can be proved in five ways. 
        The first way is motion.  Everything in motion was put in motion by something else, so there had to be some initial mover, and that was God.  Aristotle came up with the concept of the unmoved mover.  The unmoved mover moved without being moved by any prior action, and this set the universe in motion.
        The second way is the efficient cause.  Through the concept of cause and effect one can understand that if the effect exists, the cause must have existed before it. In this case, there must have been a first efficient cause to cause everything else, which we accept as God.
        The third way is from possibility and necessity.  Everything comes into existence and goes out of existence.  This means that there could have been a time when nothing existed.  Nothing can possibly have come from nothing.  God must have caused the existence of beings.
        The fourth way is the gradation of things.  Some things are better or worse than other things.  There must be something which is the best and most perfect and good, which caused all the perfection and goodness in all other things.  We call this thing God.
        The fifth way is the governance of the world.  Everything works toward some goal, but all natural beings lack intelligence.  Some intelligent being must exist that everything is directed at, and that must be God.
        Ultimately, God is the first cause of all things, so therefore he must exist.