Before you go pulling diff covers, jack the back end up, (put the car on jack stands!), put the car in neutral, and make an index mark on the driveshaft. While a helper rotates the rear tire EXACTLY one turn, count the number of turns the driveshaft makes.
Slightly more than 4 rotations? You have 4:10s (4:11 isn't a Ford Racing ratio for the 8.8). Between 3 and 3.5 rotations, you have 3.31 or 3.55s.
You say the speedo is 5-10 mph fast, but you don't say at what speed. Assuming your issue is either a gear ratio issue, or a tire diameter issue, the error will vary directly with speed, meaning as you go faster, the error will get bigger. Tire diameter can make a 5 mph difference easily at highway speeds. A gear ratio swap from 3.31-4.10 will make a MUCH bigger difference than 5-10 mph at highway speeds. For instance, on my car, 80 mph indicated represented ~66 mph actual, when I swapped from 3.31 to 3.73. Tire diameter will have some impact on that as well, but my main point is that gears would most likely have a bigger impact.
If you have the ability to adjust for tire revolutions per mile with your tuner, make that adjustment based on the tire manufacturer's published revs/mile (should be on their website). If your ratio is different than stock (based on the shade tree method described above), set that ratio in your tuner. Then, if you're still off, I'd start checking speedo issues.