An electron in a hydrogen atom undergoes a transition from an orbit...

$U = - \dfrac{{Z}^{2}}{{n}^{2}}{E}_{0}$

$Z = 1$

$U = - \dfrac{{E}_{0}}{{n}^{2}}$

$\dfrac{{U}_{i}}{{U}_{f}} = \dfrac{{n}_{f}^{2}}{{n}_{i}^{2}} = 6.25$

Taking ${n}_{i} = 2$

${n}_{f} = 5$