Turn 5 is a pain in my *ss too.
I take it by breaking early, and riding the rumbles a bit, too. Try not to let them turn the car too much, it's easy to slide around as you exit. On the exit, you should end up touching the outside rumble strip at about its mid-point. If you're hitting it sooner than that, you're apexing too early.
I usually turn in just slightly before I start braking (so that I'm braking diagonally across the track, rather that parallel to the right edge), it seems to help stop the car from running wide.
One other thing that has worked for me (sometimes, anyway) is to put the right side wheels in the dirt as you're braking, to help the car come around. It's pretty sketchy (I've kind of given up on it, because it's sooooo inconsistent)
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Ran a bunch more laps in the WRX, no improvement