Hi, I’m Chris. Welcome and thanks for asking your question!
You mentioned you have a standard transmission. The 2012 F150 does not have a manual /standard transmission option?
Can I also get the engine liter size?
4x4 or 4x2?
Gear ratio, if not known, look in the drivers door jam and give me the 2 character code under axle?
Long or short wheelbase?
The only transmission offered in the 2012 F150 is the 6R80, so regardless of which engine or 4x4 or tow package, all have the same transmission and capability.
You can tow 9400 lbs. with this truck with a drop hitch receiver.
The 5k limit is on bumper pulling. You will need a auxiliary trans cooler added and a 7 pin connector, outside of just the lights on the trailer you only need the trailer brakes. The battery charge pin and the reverse lights are not a must unless needed. You will also need a brake controller in the cab to tow your 6-7k safe
On the end of your shifter it should have tow haul button. This is used for towing It holds upshifts longer so you stay in the torque curve longer also the computer manually downshifts the transmission to aid in engine braking while towing. The tow haul on the column shift and floor shift operates the same. The manual select shift on the floor shift was not designed for trailer towing in mind.
The select shift is designed to disable the upper gears to prevent excessive shifting when traveling slow. The transmission just want to get to high gear and sometimes when doing 40mph or less this causes issues that customers do not like, so they gave them the option to have select shift and disable the higher gears. to prevent unwanted shifting. The best towing capability will come from using the tow/haul button on the shifter whether than be the button on the steering column shifter or center console shifter.
Prior to 2011 no Ford trucks had select shift but still were able to tow heavy weights.
I hope that helps to clear it up.