Mustang Backfires When Shifting At 5000 + Rpm??

It seems odd that just a header upgrade would make that much difference in your fuel curve but stranger things have happened. Find a way to test your AFR either on the dyno or on the street. If all looks decent when your in the gas and not changing gears then my suspicion would be that your valve springs are worn and are floating at elevated RPM. You should also rule out any possibilty of vac leaks, dirty IAC, or TPS out of adjustment before spending money on parts that may not be faulty. An in car fuel pressure gauge would be helpful in letting you know if the regulator is acting stupid and ramping up fuel pressure quicker/higher than it should be. I'm sure that you're already aware of the kind of havoc that an old cap/rotor, spark plugs, or wires can cause.

My only other suggestion would be to pull codes. You might get lucky.

backfiring is caused by 2 things Primarily. An extremely rich condition. Which around 5000rpm is difficult for the stock fuel system. So the other option to check into are the EGR system. Mostly the EGR. Have you ran any codes? The EGR can throw a code and not the check engine light. If thats not it (like my car) then its something like the BAP sensor or the O2's/harness.

Yes, not having cats causes that smell.