slow down on the edges and focus more on lookahead and constant turning, it is a stage you should approach not too dissimilar to F2L on a 3x3.
Mentally noting tredges that already have two pieces complete and coming back to them later will save you a ton of moves. Another way to improve efficiency and edge-pairing speed is to always solve a tredge with the same edges as those in your E layer after you complete a previous tredge.
This is easier said than done, often you'll be tempted to solve a different tredge in the U layer that seems easier. More often than not, changing your mind when edge-pairing on 5x5 is a bad idea.