Answer
4.18 eV.
Work Step by Step
Equation 41.45 gives the energy of an atomic level, taking screening into account.
It is given in terms of n and $Z_{eff}$ by $E_n=-\frac{Z_{eff}^2}{n^2}(13.6 eV)$.
Find the energy of the 5s electron.
$E_{5s}=-\frac{2.771^2}{5^2}(13.6 eV)=-4.18 eV$
The ionization energy is the energy needed to free the weakest-bound electron, so the ionization energy is 4.18 eV.
