A320 FLC OVERSHOOT ASSIGNED ALT DUE TO EVASIVE MANEUVER FROM C90 ISSUED XING C172.

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DEPARTED RWY 4L ORD; 140 DEG HDG; CLB TO 5000 FT. CLBING THROUGH ABOUT 3000 FT; ATC SAID VFR TFC 12 O'CLOCK; 5500 FT. I DID NOT HEAR THE DISTANCE. MY FO LATER SAID IT WAS 5 MI OUT. I SHALLOWED MY CLB RATE WHILE ACCELERATING TO 250 KTS. WE WERE THEN GIVEN A R TURN; 180 DEG HDG ABOUT THE TIME I REACHED 4500 FT. AT SOME POINT WE HAD AN AMBER ALERT TCASII FOLLOWED BY 'REDUCE VERT CLB.' MY FO VISUALLY SPOTTED A LIGHT CESSNA ABOVE TO THE R AT 1-2 O'CLOCK POS. I WAS SOMEWHAT DISTR IN THE TURN AND CLBED TO 5250 FT WHILE LOOKING; BUT NEVER SAW THE VFR TARGET. I THINK ANOTHER UPDATE BY ATC BEFORE GIVING US THE TURN WOULD HAVE BEEN BETTER. WE THOUGHT ATC WAS GIVING US THE TURN AFTER PASSING THE TARGET. SUPPLEMENTAL INFO FROM ACN 502801: DEP GAVE US A HG OF 180 DEGS. AT THIS TIME I HAD THE TFC IN SIGHT; AND WE PASSED DIRECTLY UNDERNEATH A C172. AS I LOOKED BACK INSIDE AFTER THE TFC WAS PAST US; I NOTICED WE STILL HAD A SLOW (200-300 FPM) CLB; AND WERE PASSING 5100 FT. I POINTED TO THE ALT WINDOW AND REMINDED THE CAPT (PF) THAT WE WERE ASSIGNED 5000 FT.