A CE560 FLC OVERSHOT ALT BY 500 FT. PLTS AND ATC NOTICE; THEY RETURN TO ASSIGNED ALT.

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AFTER LEVEL OFF AT 5000 FT ON DEP; ATC GAVE US DIRECT TO A FIX NOT ON OUR CLRED RTE. I LOOKED DOWN TO THE CHART TO FIND ITS FREQ; THEN HEARD THE BEEP OF THE ALT ALERTER. I LOOKED UP TO FIND US CLBING THROUGH 5300 FT. I TOLD THE FO (WHO WAS FLYING) TO DSND. ATC SAID THEY SHOWED US AT 5500 FT AS WE DID SO. WE CORRECTED BACK TO 5000 FT AND CONTINUED WITH THE FLT. THE FO; NEW TO THE AIRPLANE; SAID HE WAS DISTR BY AIRSPD AFTER THE LEVEL OFF AND FAILED TO NOTICE THE ALT. I WAS DISTR FROM SUPERVISING HIM BY THE UNEXPECTED CLRNC REVISION RIGHT AFTER TKOF. SUPPLEMENTAL 572184: I LEVELED OFF AT 3000 FT; AND WAS IMMEDIATELY CLRED TO CLB TO 5000 FT; I THEN CONTINUED THE CLB AND UPON REACHING 4000 FT MSL; BEGAN TO INCREASE MY AIRSPD TO 250 KIAS. WE WERE THEN CLRED DIRECT TO JFK VOR; WHICH WAS NOT ON OUR FLT PLAN OR CLRNC. IN THE L CLBING TURN; I NOTICED THE AIRSPD INCREASING RAPIDLY AND PITCHED UP TO MAINTAIN BELOW 250 KIAS. AT THIS TIME; I NOTICED I WAS ALSO AT MY ASSIGNED ALT OF 5000 FT MSL. IMMEDIATELY; I LOWERED PITCH AND REDUCED PWR WHEN THE ALT ALERTER RANG (300 FT ABOVE SELECTED ALT). FO RECENTLY CAME OFF A 5-WK BREAK IN FLYING. FO HAS LOW TIME IN ACFT TYPE (130 HRS TOTAL). I SHOULD HAVE ACTIVATED THE AUTOPLT TO ASSIST IN WORKLOAD REDUCTION. I SHOULD HAVE MAINTAINED A SLOWER AIRSPD AND CLB RATE DUE TO THE LOW ALT OF OUR CLRNC.