The transition from the state $n=4$ to $n=3$ in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:

The energy of radiation emitted is $\Delta E\propto \left(\frac{1}{n_f^2}-\frac{1}{n_i^2}\right)$.Ultraviolet (UV) radiation has higher energy than Infrared (IR) radiation. For IR radiation, we need a transition with lower energy than the $4\to 3$ transition.In the options:$2\to 1$ is Lyman series (UV).$3\to 2$ and $4\to 2$ are Balmer series (Visible/UV).$5\to 4$ is Brackett series, which corresponds to much lower energy and falls in the Infrared region.Generally, as the principal quantum numbers $n$ increase, the energy gap between adjacent levels decreases. Thus, $5\to 4$ has less energy than $4\to 3$.