PREMIER 1 FLT CREW TCAS RA DEPARTING ON THE TEB 5 CAUSING CLB ABOVE 1500 FT INITIAL ALT RESTR.

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THE SITUATION DEVELOPED AFTER DEPARTING RWY 24 AT TEB. THE ASSIGNED DEP PROC WAS THE TEB 5 DEP; WHICH IS A CRITICAL PROC THAT HAS BECOME SOMEWHAT INFAMOUS FOR DEVS. DUE TO ARRS INTO A LARGER ARPT TO THE S; INITIAL CLBS ARE RESTR TO 1500 FT MSL; A TURN TO THE W; AND A FURTHER CLB WITHIN 4.5 MILES OF THE TEB VOR. KNOWING THAT THIS DEP WAS CRITICAL; I BRIEFED IT TO THE SIC; AND HE BRIEFED IT BACK TO ME. WE PROGRAMMED THE PROC IN THE FMS; AND ARMED THE FLT DIRECTOR TO 'FLY' THE PROC. WE WERE NOT RUSHED AS A CREW BECAUSE WE HAD A DELAY OF OVER 30 MINS FOR WX ON OUR DEP RTE. WE ALSO ROUTINELY OPERATE OUT OF TEB. DURING OUR DELAY; I HEARD A SINGLE ENGINE CESSNA COMMUNICATING WITH THE TOWER ABOUT FLYING IN THE VICINITY FOR AERIAL PHOTO WORK. WHEN WE WERE CLRED FOR TAKEOFF; TOWER ADVISED US THAT A CESSNA WAS FLYING OVER AN INTERCHANGE ON A HWY. I CONCLUDED THAT THE INTERCHANGE WAS S OF THE ARPT IN THE VICINITY OF OUR DEP; BUT I ASSUMED THAT IT WOULD NOT BE AN IMMEDIATE CONFLICT OFF THE RWY. UPON OUR DEP; CLBING OUT OF APPROX 1000 FT MSL; THE TCAS CALLED 'TRAFFIC; TRAFFIC.' I BEGAN TO LOOK FOR THE TRAFFIC VISUALLY WHILE PAYING ATTENTION TO THE CRITICAL DEP PROC. AT APPROX 1300 FT MSL; THE TCAS CALLED 'MONITOR VERTICAL SPEED;' AND I SAW THAT I NEEDED TO INCREASE MY CLB RATE. ALMOST IMMEDIATELY; THE TCAS CALLED 'CLIMB; CLIMB.' I WAS AT 1400 FT MSL AND KNEW I WAS GOING TO DEVIATE FROM THE DEP PROC TO COMPLY WITH THE TCAS. WE HAD JUST BEEN HANDED OFF TO NY DEP CTL; AND THE SIC IMMEDIATELY INFORMED THEM OF THE REQUIRED DEVIATION OF CLBING INTO DEP CTL'S AIRSPACE. ABOVE 1600 FT BUT BELOW 1700 FT MSL; TCAS CALLED 'CLEAR OF CONFLICT.' WE INFORMED ATC THAT WE COULD RESUME THE REQUIRED 1500 FT MSL; BUT THEY GAVE US A FURTHER CLB AND A HEADING. ATC ASKED IF TOWER INFORMED US OF THE TRAFFIC; AND I REPLIED IT WAS A TCAS RA. ATC HAD NO FURTHER COMMENT. I NEVER HAD VISUAL CONTACT WITH TRAFFIC. THE DEP FROM RWY 24 AT THIS ARPT IS A VERY BUSY PROC IN VERY BUSY AIRSPACE. NOT ONLY IS THE TEB 5 DEP CRITICAL; IT IS ALSO A NOISE SENSITIVE RWY WHICH CAN BE OF CONCERN TO MANY JET ACFT. ONCE AIRBORNE; YOU HAVE TRAFFIC ABOVE AND BELOW YOUR ACFT. WITH THE TEB 5 BEING SO CRITICAL; IT IS HARD TO BREAK FROM IT UNDER ANY CIRCUMSTANCES. PLTS SHOULD BE READY FOR THE MENTAL SHOCK OF BREAKING AWAY FROM A HEAVILY EMPHASIZED PROC TO COMPLY WITH THE REQUIRED CALLS OF THE TCAS SYSTEM SHOULD THEY ARISE.