You should not be shifting into 5th at all at the track. Stay at the top of 4th, that is where you want to be crossing.
You want to take corners? Not going to happen on the stock 4 link. TA/PHB setup or swap to IRS. Either way is going to be about $2k-$3k because the TA/PHB setup is not cheap and if you get an IRS you need to pull it COMPLETELY apart and redo every bushing and piece of rubber in it with delrin and poly or it'll be a wheel hopping nightmare.
2000 Mustang GT Steeda #0048 34k miles. 99 Cobra 4V swapped, FTBR IRS swapped, exhaust, tuned by James Gordon.
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.