1. **State the problem:** We have a right triangle $\triangle KLM$ with $\angle M = 90^\circ$, and side lengths $ML = 65$, $LK = 97$, and $KM = 72$. We need to find the sine of $\angle L$. 2. **Recall the sine definition:** In a right triangle, $\sin(\theta) = \frac{\text{opposite side}}{\text{hypotenuse}}$. 3. **Identify the hypotenuse:** The hypotenuse is the side opposite the right angle $M$, which is $LK = 97$. 4. **Identify the side opposite $\angle L$:** The side opposite $\angle L$ is $KM = 72$. 5. **Write the sine ratio:** $$\sin(L) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{KM}{LK} = \frac{72}{97}$$ 6. **Final answer:** The sine of $\angle L$ is $\boxed{\frac{72}{97}}$.