If the T5 to T3/T1 shuttle bus is back in service when the itinerary is taking place, OP may be able to use that service.
I believe a boarding pass for the UA domestic flight would be required to be in hand. Clearing security at T5 at that time
of the evening is likely to be quick and less of a risk than back at T1. But bus schedule, even if running, might be a factor,
as it wasn't all that frequent.
https://www.flychicago.com/ohare/Ser...Pages/ATS.aspx