C and E are connected. I believe there is a shuttle bus from A to C that you can use so you do not need to leave the sterile area, so take it to C and then walk to your gate in E. The other option in the inter-terminal train. It will take you from A to E, however you will need to go back through security if you take it. They are extending the "terminal-link" above ground train to terminal A - but I don't think it is finished yet.