You can’t walk airside. I read somewhere that you can technically enter T3 with your boarding pass as ORD will let you enter any terminal. You can then either go landside again and take the train to T5 and re-clear security or there is apparently an irregular airside bus between terminals. It seems like a lot of trouble though. Maybe if you get stranded for 7h like the OP it might make sense.

Apparently the reason CX arrives in T5 is that in ORD only T5 can handle international arrivals. AA and BA then have their planes towed to T3.