Find the smaller angle between the hour and minute hands of a clock at $5:24$.

The standard formula to find the angle $\theta$ between the hour hand and the minute hand of a clock is:
$$\theta =\left|30H-\frac{11}{2}M\right|$$

Given time is $5:24$, where:

* Hour ($H$) = $5$
* Minute ($M$) = $24$

Substitute the values into the formula:

$$\theta =\left|30(5)-\frac{11}{2}(24)\right|$$

$$\theta =|150-11\times 12|$$

$$\theta =|150-132|$$

$$\theta =18^{\circ }$$

The smaller angle between the hour and minute hands at $5:24$ is $18^{\circ }$.