I have a 2013 f150 xlt with stock 17x7.5 rims. I currently have the handkook tires on now but I was wondering what the maximum tire size is that I could put on the rims.

 

First word of advise, give the search tool a try, there are tons of info on subjects like this.
Next, is your truck 2 or 4 wheel drive, and is it all stock or have some for of level/lift installed? Lastly the limiting factor of overall tire size for that particular rim will be width, try to not go any wider than a 12.5" wide tire, if all stock height will be between 31.5-33" depending on 2 and 4 wheel drive.