I have a 2013 5.0 automatic with the stock 3.15 gears and I have started having what I believe to be transmission issues. I don't know if it is the transmission, the torque converter, or the rear end starting to go out.
I have brought it to my local Ford and a local transmission shop, and according to Murphy's Law, the car never acts up, even when I take a technician along for a ride to try and troubleshoot the car.
I have experienced my first to second gear shift taking a lot longer than normal and when I am in sport mode, whenever I tell it to shift to fourth from third, it will slip for a second or two before it "finds" fourth gear.
So, I have started tossing a camera underneath my car in hopes that I can catch the noise during a cold startup in the morning. My first video is a short one, and I will keep recording until I can seem to pinpoint the noise and capture a much better "noise."
The link to the clip I have recorded is here.
You can definitely hear, if you listen, right around the three second mark as the rpm's are ramping back down from a cold start, a grinding noise.