Thank you all soo much! I forgot to include the most important part of my query:
Qatar and United no longer interline, and the bags will therefore only be tagged from DOH to ORD (QR), so I have to collect them in T5 and do the check-in with UA in T1

. On the way back, UA will only tag PDX to ORD, and I will have to schlepp the bags from T1 to T3.