Your math is a little out. After 7 generations, it is 0.78%. 5 generations after 1788 and assuming unbroken paternal and maternal linkages are unbroken, it is less than 1%.
You need a reference point to compare the dna of present day people with at least 2 generations or more before 1788. Unfortunately, I don't think that a representative sample from 2 generations or longer before 1788 exists or hasn't been found yet.
