I can't guarantee that this will fix it but a great deal of problems come down to these two things. There are other common faults such as some nylon check balls in the valve body that melt and failure of an aluminium clutch hub. But if the box has only covered between 100,000 and 200,000km without serious abuse it will more than likely be fluid and / or solenoid.
If you read the EL manual it says that these boxes are sealed for life and dont require a fluid change unless they tow. So chances are if it has been hanbook serviced all it's life it has never had a fluid change. Mine resembled black treacle when I did it by my car tows a hefty ski boat during the summer so it is fairly well abused. If you get a trans service they will drop the 4 litres in the pan and change the filter, leaving 12 odd litres still in the torque convertor and lines. You can do a full flush yourself by dropping the cooler supply line into a bucket and pour fresh fluid into the trans filler while running at idle to use the trans pump to transfer the fluid. There have been a couple of detailed threads written before by me, gregaust and somone else I cant remember. Or you can take it to a good trans specialist and have them do it for not much more than the cost of the fluid.
The S5 solenoid controls or modulates the line pressure during shifts. It is prone to overheating and failure where it is slow to react to it's input voltage. Swapping this often resolves 1-2 and 2-3 shift flaring. When you drop the pan to do the filter you will see all the solenoids marked quite clearly and it is just a matter of swapping it out. For warranty sake I had mine done by a shop. Dont try and get it from Ford though - they quoted me $695 for the solenoid. I understand that $200 or so is the real going price from trans shops.
Like I said - I cant guarantee it but it has resolved the issue for a lot of people and is a known common fault.