1. **State the problem:** Identify which angles are adjacent to angle $\angle 5$ in the given figure. 2. **Recall the definition of adjacent angles:** Adjacent angles share a common vertex and a common side but do not overlap. 3. **Analyze the figure:** $\angle 5$ is formed between the downward vertical ray and the rightward slanted ray. 4. **Check each angle for adjacency:** - $\angle 1$ shares a common side with $\angle 5$ and the vertex, so it is adjacent. - $\angle 2$ does not share a side with $\angle 5$. - $\angle 3$ does not share a side with $\angle 5$. - $\angle 4$ shares a common side with $\angle 5$ and the vertex, so it is adjacent. 5. **Conclusion:** The angles adjacent to $\angle 5$ are $\angle 1$ and $\angle 4$. **Final answer:** $\boxed{\angle 1 \text{ and } \angle 4}$