Turns out the guy misread the email from Trek. He thought it said 56cm. He said that Trek usually ships the same size frame as the one you broke.
They tried to fix the derailleur hanger on my 5200, but when they pulled the dropout out they noticed some fractures inside the either the seat stay or chain stay tube where the hanger was glued. So the 5200 frame is dead.
They are offering me a new frame, either a Madone 5 or a Domane 5. I'll probably get the Domane. For an extra $800 I can upgrade to the Domane 6 frame. I'm considering that. But I want to stop by the shop first and take a 58cm Domane for a spin to see if a 58cm would fit me. If not I'll go for the 60cm.
The other issue is my crank and BB. The crank on my 5200 is an old Octalink Ultegra 6500, and the BB is a Dura-Ace 7700 cartridge style BB. Neither of those will fit the new frame, which is BB90. So I'm looking at having to upgrade the crank and BB as well. I asked about putting a new Ultegra 6800 crank and BB on the bike but according to the guy at the shop the Ultegra 6800 isn't compatible with a 9-speed drivetrain. So I'm looking at having to upgrade the entire drivetrain,
I'm thinking of just getting the Domane 6 frame for now and waiting until the fall/winter before buying a groupset for it and kind of turn it into a winter bike build project. It's not like I won't have another bike to ride this summer (I have another thread on this board about that).