ALT DEV; ALT EXCURSION ON THE TEB 5 DEP PROC WHEN A C560 FLT CREW CLBS THROUGH THE ASSIGNED ALT PRIOR TO THE 4.5 DME OF TEB.

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DEPARTED RWY 24 AT TEB ON TEB 5 SID. LEVELED AT 1500 FT AS DIRECTED; TURNED TO 280 DEG HDG AS DIRECTED; BEGAN CLBING TO 2000 FT PREMATURELY. PNF ADVISED OF DEVIATION AND CORRECTION TO 1500 FT WAS APPLIED. ACFT WAS AT 1900 FT WHEN CORRECTION WAS MADE. ON THE SID; CLB TO 2000 FT IS REQUIRED UPON REACHING 4.5 DME TEB. I STARTED THE CLB WHEN ESTABLISHED ON THE 280 DEG HDG. THIS SID HAD BEEN BRIEFED COMPLETELY; BOTH PF AND PNF ARE VERY FAMILIAR WITH THE PROC. NO TA OR RA WAS RECEIVED; NOR DID ATC QUERY US ON THE DEV. THE LCL CTLR DID ASK US TO CHANGE FREQUENCIES JUST AS I TURNED TO 280 DEGS; WHICH TIED UP THE PNF AT A CRITICAL MOMENT. STILL; I SIMPLY FORGOT THE 4.5 DME RESTRICTION. SUPPLEMENTAL INFO FROM ACN 628724: AS PIC; I WAS IN THE R SEAT AS THE PNF. THE SIC (FO) WAS BRIEFED BEFORE TKOF ON THE DEP PROC FOR THE TEB 5 OFF RWY 24. AFTER TKOF CLBING THROUGH 500 FT; I CALLED; 'ONE THOUSAND TO GO.' APCHING 1500 FT; I CALLED; '1500 FT.' THE PF CONTINUED TO CLB; AND AFTER I CALLED '1500' AGAIN; THE CLB WAS LEVELED OFF AT 1800 FT. DSCNT WAS INITIATED; FOLLOWED SHORTLY BY A CLB TO MAINTAIN 4000 FT ISSUED BY DEP. NO TCAS TA OR RA WAS ISSUED. THE SIC LATER SAID THAT HE HEARD MY CALLOUTS; BUT THEY WEREN'T REGISTERING.