1. **State the problem:** Find the area of a triangle with base $14$ and height $5$. 2. **Formula:** The area $A$ of a triangle is given by the formula: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Substitute the values:** $$A = \frac{1}{2} \times 14 \times 5$$ 4. **Calculate:** $$A = \frac{1}{2} \times 70$$ 5. **Simplify:** $$A = \cancel{\frac{1}{2}} \times \cancel{70} = 35$$ 6. **Answer:** The area of the triangle is $35$ square units.