An example for $n=7$ is given in  J. W. S. Cassels, Factorization of polynomials in several variables, Proc. Fifteenth Scandinavian Congress (Oslo, 1968), vol. 118, Lecture Notes in Mathematics, Springer, Berlin, pp. 1-17. This reference is from https://oeis.org/A112090 and is quite technical.

here I type the example from the paper in a sort of computer-readable format

    l=(1+sqrt(-7))/2
    m=(1-sqrt(-7))/2
    # t a nonzero(?) parameter
    f(x)-g(y)=(x^3+l*x^3*y-m*x*y^2-y^3-(3*l+2)*t*x+(3*m+2)*t*y+t)*
              (x^4-l*x^3*y-x^2*y^2-m*x*y^3+y^4+2*(m-l)*t*x^2-
               7*t*x*y+2*(l-m)*t*y^2+(3-l)*t*x-(3-m)*t*y-7*t^2)