1999 LEXUS RX Engine Problems

WHEN DRIVING MY LEXUS RX 300 1999 IT FEELS VERY FORCED AND WHEN ON THE EXPRESS WAY THE RPM GOES UP TO 5 WHEN IM DRIVING 60MPH AND WHEN I COME TO A COMPLETE STOP AND ITS TIME TO GO MY CAR STALLS AS IF IT WAS IN NEUTRAL VERY SCARY WHEN I HAVE MY NEWBORN AND A 7 YEAR OLD IN THE CAR. I HAVE MAINTAINED MY CAR TO THE UPMOST STANDARDS FROM THE BEST GAS SYNTHETIC OIL CHANGES CONSTANTLY CHECKING EVERYTHING IS IN GOOD CONDITIONS . FOR A LEXUS I AM VERY UPSET BECAUSE MY MECHANIC HAS SAID ITS THE TRANSMISSION AND THAT I WILL HAVE TO REPLACE IT WHICH COSTS 4-5,000 DOLLARS AND I MEAN IS A 15 YEAR OLD CAR WORTH PUTTING 5 GRAND INTO IT? I EXPECTED THIS CAR TO LAST ME A LITTLE BIT LONGER I MEAN FROM WHAT I WAS TOLD THIS CAR...