When you come in: Interline stuff doesn't matter. You can check in at T5 itself. Whether your bags are checked through or not, you pick them up at T5, clear customs, and then check in with the UA counter within T5, before leaving the secure area. It is immediately after the customs, very hard to miss, but if you happen to see people waiting to receive arriving pax, then you have gone too far and should turn right back. They'll print new tags for your bags and, if necessary, BPs for you.

After this, find your way to the free Airport Transit System train and go to T1. You'll need to clear security again, so allow plenty of time for that, not that there is much to distract you at ORD terminals.

When you return: If UA won't interline, you'll have to take your luggage to T3. My own preference would be to walk the long walk with a luggage cart. However, there is also the airport train if you would prefer---you'll need to change floors 4 times, remember to look for elevators. (Thanks to HNL for reminding me that QR leaves from T3, a detail I had missed though it is mentioned in the OP.)