In addition to Jon's rather more in-depth replies to my own (

), something that can be a cool exercise to develop your chord-lead relationships in a more interesting way is to take the chords, extend them, and then play those extended arpeggios over the first basic chords. This song is probably not a great one to start with; basic rock ballads are best.
So, say you have something that goes A5, C5, G5. The first easy step is to work out what those fifth chords are implying in the context of the song. The full, non-extended, chords would be Am, C major, G major. Extending them by adding the 7ths and you'd have Am7, Cmaj7, G7, which would probably sound like crap if played over a rhythm comprised of fifth chords.
So, we keep going and extend the chords in ways that make them sound appropriate. You might do something like this:
|----3----x----5----
|----1----5----5----
|----1----4----4----
|----x----5----3----
|----0----4----x----
|----x----x----3----
Hopefully someone will correct me if I mangle the chord names here. (I'm just returning to music after a long absence. I used to teach, but that was years ago). Anyways, I would call those chords Ammaj9, Cmaj7b9 (inverted), G13.