What size tires?
#18
You're really limiting your options without installing a leveling kit. However, the biggest tires I know of anyone putting on an F-150 without a leveling kit are 305/65/18 which equates to about a 34". The truck was an FX4. There was no rubbing that I know of but it was mighty close. You should be able to find plenty of tires that fit the stock 7.5" rim width. I know for a fact that you can fit 12.5" tires on the 7.5" rim without a problem. Just keep in mind that the wider the tire you get without using a wider rim, the tire is going to have a "doughnut effect," meaning it appears rounder than it should.