The recoil speed of a hydrogen atom after it emits a photon in going from n=5 state to n=1 state will be :

$\text{Applying Conservation of Momentum,}$

$\begin{array}{l}{P}_{\text{atom }}=P_{\text{photon }}\\ \Rightarrow M{V}_{\text{recoil }}=\frac{h}{\lambda }=Rh\left[\frac{1}{1^2}-\frac{1}{5^2}\right]\\ V_{\text{recoil }}=\frac{Rh}{m}\left[\frac{24}{25}\right]=\frac{1.09\times {10}^7\times 6.63\times {10}^{-34}\times 24}{1.67\times {10}^{-27}\times 25}\approx 4.17{\mathrm{ms}}^{-1}\end{array}$