There is a Gino's East pizza one stop away from the airport in Rosemont on the red line. Might be tight with only 5 hours to spare to get to downtown and back as that ride takes about 45 min - 1 hour each way on the red line. You could probably take an uber but according to Google maps, it's about a 25 min drive without traffic.
I'm a native New Yorker but have no shame in enjoying deep dish when in the windy city.
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