Can you give a few more details about the current deck and the plan for the new deck?
*Are you saying cut off the joists at the beam? (ie cut off the 5 foot cantilever..)
*Then where does the new deck go? - Are you setting up another post/beam farther out?
I would just sister the joists. Don't cut them off - just add the new ones next to the old ones and have a 5 foot overlap. (So the new joists will sit on the same beam as the old joists.) The only places it will be noticeable is underneath and in the deck/screw pattern... and it will be hardly noticeable at that.