1. **State the problem:** We need to find the volume of a rectangular prism with length $l = 8$ cm, width $w = 3$ cm, and height $h = 5$ cm. 2. **Understand the formula:** The volume $V$ of a rectangular prism is calculated by multiplying its width, height, and length: $$V = w \times h \times l$$ 3. **Substitute the values:** Replace $w$, $h$, and $l$ with the given dimensions: $$V = 3 \times 5 \times 8$$ 4. **Calculate the volume:** $$V = 15 \times 8 = 120$$ 5. **Conclusion:** The volume of the rectangular prism is $120$ cubic centimeters.