Need to extend some cat5e, best way..

I've got an old waiting closet that's getting redone. New rack, patch panels, etc... but keeping existing cat5e wire..

95% of the cables have enough slack to reach the new panels. For those that don't, what's the best way to extend?

My plan was to terminate the 20 or so short ones to a standard 110 block. Then punch down a new cat5e from that block to the new panel.

Will that pass testing?