The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by $E_n = -R_H \left( \frac{1}{n^2} \right)$, where $R_H = 2.18 \times 10^{-18}$ J. The radius of the $n^{th}$ orbit is given by $r_n = n^2 a_0$, where $a_0 = 52.9$ pm. By substituting $n = 5$ into these formulas, we can find the energy and radius of the fifth orbit.