1. **State the problem:** We need to find the area of an isosceles triangle with two equal sides of length 5 cm and an included angle of 65° between them. 2. **Formula used:** The area $A$ of a triangle with two sides $a$ and $b$ and included angle $\theta$ is given by: $$A = \frac{1}{2}ab\sin(\theta)$$ 3. **Apply the formula:** Here, $a = 5$ cm, $b = 5$ cm, and $\theta = 65^\circ$. 4. **Calculate the area:** $$A = \frac{1}{2} \times 5 \times 5 \times \sin(65^\circ)$$ 5. **Evaluate $\sin(65^\circ)$:** Using a calculator, $\sin(65^\circ) \approx 0.9063$. 6. **Substitute and simplify:** $$A = \frac{1}{2} \times 25 \times 0.9063 = 12.5 \times 0.9063$$ 7. **Final calculation:** $$A \approx 11.3$$ 8. **Answer:** The area of the isosceles triangle is approximately **11.3 cm²** to 1 decimal place.