Happy Rob,
Since this post is a few days old, you may have already completed your bike/trailer wiring setup. If you haven't, and since your bike is wired with a brand new 5-pin round, In my opinion, for whatever it's worth, would be for you to simply cut the 4-pin flat off the trailer and purchase the 5-pin round mate for your new bike end plug. Then simply mate up pin to pin and wire to wire for a neat, clean and well done NEW system. That way, there's no adapters, no additional potential problems due to too many connections that are not needed. I like clean and simple.
Scott