AN SF34 CREW OVERSHOT ASSIGNED ALT DURING DEP.

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DURING CLBOUT; STL DEP ISSUED A CLRNC TO US TO CLB TO 5000 FT. AT 4000 FT; BOTH PLTS ACKNOWLEDGED 1000 FT TO GO BY POINTING TO THE ALT PRESELECT; HEARING THE ALT AURAL CHIME AND BOTH PLTS STATING; '4000 FT FOR 5000 FT.' AS PNF; I WAS OBLIGATED TO CALL DEP TIMES AND FUEL LOAD IN TO OUR COMPANY OPS WHEN WORKLOAD PERMITS. THINKING THE WORKLOAD PERMITTED; I TOLD THE FO 'I'M OFF COM #1 TO CALL IN TIMES. WE HAVE LESS THAN 1000 FT TO GO TO LEVELOFF; ON THE 070 DEG HDG; ARE YOU OK?' THE FO RPTED HE WAS OK AND HAD THINGS UNDER CTL. WHILE I WAS ON COM #2 CALLING TIMES AND VERIFYING FUEL LOAD BY LOOKING AT THE RELEASE; I HEARD THE AURAL ALT CHIME GOING OFF. I NOTICED THAT 5000 FT WAS STILL IN THE ALT PRESELECT BOX AND THE ACFT WAS APCHING 5500 FT. I QUICKLY CALLED THIS TO THE FO'S ATTN BY VERBAL ACKNOWLEDGEMENT; POINTING TO ALTIMETER AND PUSHING THE YOKE OVER. THE FO QUICKLY DSNDED TO AND LEVELED OFF AT 5000 FT. I RPTED TO THE FO THAT 'I'M BACK ON COM #1; LET'S WAIT TO SEE IF ATC CALLS US ON IT' (THE CLB THROUGH ALT ASSIGNED). ATC NEVER CALLED US ON IT; NOR DID THEY ACKNOWLEDGE ANYTHING. I FILLED OUT A NASA RPT JUST TO BE ON THE SAFE SIDE. SUPPLEMENTAL INFO FROM ACN 505390: ON THE EVENING OF MAR/XA/01 AT XA00; I DEPARTED STL WITH MY CAPT IN ACFT ABC; WHICH WAS A COMPANY FLT; DEST FWA. UPON INITIAL CONTACT WITH DEP CTL; WE WERE ASSIGNED AN EASTERLY HDG ASSIGNMENT AND AN ALT OF 5000 FT MSL. I WAS OPERATING AS THE PNF AND MY CAPT WAS THE PF. AS WE CLBED; A CTL CHANGE WAS AGREED UPON BY BOTH OF US SO THAT THE CAPT COULD ATTEND TO A COM WITH OPS. THE CTL EXCHANGE OCCURRED PRIOR TO THE TIME WE NEEDED TO LEVEL OUR ALT AT 5000 FT MSL. DUE TO THE EXCHANGE OF THE CTLS; I INADVERTENTLY ALLOWED THE ACFT TO CLB THROUGH OUR ASSIGNED ALT BY APPROX 250-300 FT ABOVE 5000 FT MSL. IN THE FUTURE; THIS PROB MAY MOST CERTAINLY BE AVOIDED BY DELAYING A CHANGE OF CTLS UNTIL OUT OF A CRITICAL PHASE OF FLT. THE ALTDEV OCCURRED FOR NO MORE THAN 30-45 SECONDS BEFORE CORRECTED.