AFTER LNDG LONG AND ROLLING TO THE FAR END OF RWY 11; THE CL60 CREW WAS INSTRUCTED TO TURN OFF AT THE NEXT (LAST) EXIT. THE PLT TURNED OFF ONTO RWY 5-23.

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THIS WAS A DEADHEAD PORTION OF A FLT AND THE FO WAS THE PF. THE FO HAS LESS THAN 10 HRS EXPERIENCE IN THE AIRPLANE. THE FO WAS ABOUT 5 KTS OVER VREF AND LANDED LONG AND DID NOT APPLY THE BRAKES EARLY. AT NO POINT WERE WE IN DANGER OF ROLLING OFF THE END OF THE RWY. HOWEVER; WE ROLLED TO VERY NEAR THE END. THE TWR CTLR WAS NOT BUSY AND WAS VERY CASUAL WITH HIS HANDLING OF US. THE CTLR SAID; 'I SEE YOU HAVE ROLLED LONG; THAT MEANS YOU MUST BE GOING TO THE FBO AT THE END OF THE RWY.' I TOLD THE FO THAT WE WERE GOING TO ZZZ AVIATION AND THAT WE HAD PASSED IT DURING THE LNDG ROLL. THE TWR CTLR THEN SAID; 'EXIT THE RWY AND STAY WITH ME.' I DID EXACTLY THAT BY MAKING THE VERY NEXT L ONTO RWY 5 (WE HAD LANDED ON RWY 11). THE CTLR THEN SAID HE MEANT FOR ME TO TURN L AT THE END OF THE RWY AND THAT RWYS 5/23 WERE ACTIVE AND IN THE FUTURE IF I WANTED TO TAXI ONTO THEM I SHOULD ASK. THE ISSUE THAT TROUBLED ME IS THAT OUR LNDG ROLLOUT TERMINATED RIGHT WHERE RWYS 11 AND 5 INTERSECT. IF RWY 5 WAS REALLY ACTIVE WE WERE AT TAXI SPD AND XING OVER RWY 5 WHETHER WE TURNED ONTO IT OR MERELY TAXIED ACROSS IT. EITHER WAY WE WERE VERY NEARLY AT A STOP AND WERE LINGERING AT THE INTXN OF THE 2 RWYS FOR SEVERAL SECONDS.