The aim of this paper is to present the method of resolution of the algebraic equation of 5° degree in the Bring's form $x^5 + 5x - a = 0$, where $a$ is a non-zero complex number, which appears in the third volume of monumental work “Lehrbuch der Algebra” by H. Weber. Weber finds the solutions as rational functions of certain values of an elliptic modular function, introduced by Weber himself to compute the Hilbert class field of an imaginary quadratic field, in a point of the complex upper half plane whose dependence on $a$ is explicitly given.