… can be its own derivative

$f(x)$ can be its own derivative. In the infinite polynomial $f=1+x+\frac{1}{2}{x}^2+\frac{1}{6}{x}^3+$ ______, what numbers multiply $x^4$ and $x^5$ if $df/dx$ equals $f$?

This exercise has fill-in blanks from its source book and no answer key.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.2 Powers and Polynomials, #35