Yes that is correct. As soon as you walk through the doors to get landside all of the major carriers have desks setup just to recheck bags to your onward journey. I am usually flying AA but I believe UA is at the end of the hallway to the right.

You could, in theory, take your bags with you to terminal 1 and check them there but you will then be competing with everyone trying to check in who is starting their journey so T5 is usually quicker for bag drop.