So I'm not sure what the 5* challenge is like now, but I completed the 6* challenge without calling in my last reinforcement (Phantom), so maybe this will help:
Starting lineup was Biggs, Wedge, Fives. Reinforcements used were Ghost and JC. I had to do the challenge a few times until I got good enough RNG.
I'm not sure if you're fighting Mace or Tarkin in the 5* challenge. If Mace, I found the key was to get JC really low on health before a Clone could taunt, then bring in Ghost to AOE and kill JC off. Then after that it was all about using Ackbar to keep healing Biggs so Biggs could keep soaking up damage. If Tarkin... I have no words of wisdom yet, but similar concept of keep Biggs taunting/keep Biggs healed applies.
To the OP: try starting with Biggs, Clone Serg, and Phantom. Phantom can provide target lock for Biggs; Clone Serg can taunt and soak up some of the damage if Biggs loses taunt or doesn't land a TL. Reinforce with Ghost if you need an AOE kill; reinforce with JC if your ships are getting low on health and you need a heal. The biggest weakness in your lineup is that Clone Serg and JC both hit like wet noodles, so you're really going to need your other three to deal out serious damage. Also, Clone Serg is low on gear to be the tank he needs to be... I'd work on that a bit. Finally, throw a whole pile of resources into Biggs' ship. He's still very OP after this ship rework, plays well with just about everyone, and is part of a team to get Chimaera, so it's worth maxing his stars, level, and abilities.