The CLE-ORD flight will come into one of the other terminals, so she could easily hit one of those up as a partner flight. What airlines is she flying?
Double-check it's T5 as well. UA/ANA go out of T1, AA/JAL go out of T3. Asiana, Cathay, and Korean go out of T5.
Assuming the OP is correct that the flight leaves from T5, the better thing to do for me would be to do the transfer first, go back through security, and then settle into a lounge at T5. The lounges are past security so all the pax needs to do is walk to the gate from the lounge. Much better, IMHO.