1. **State the problem:** We need to find the value of $F$ given the formula $$F = \frac{2(v^2 - u^2)}{3}$$ and values $u = -8$, $v = -5$. 2. **Substitute the values:** $$F = \frac{2((-5)^2 - (-8)^2)}{3}$$ 3. **Calculate the squares:** $$(-5)^2 = 25$$ $$(-8)^2 = 64$$ 4. **Plug these into the expression:** $$F = \frac{2(25 - 64)}{3} = \frac{2(-39)}{3}$$ 5. **Multiply numerator:** $$2 \times (-39) = -78$$ 6. **Divide by 3:** $$F = \frac{-78}{3} = -26$$ **Final answer:** $F = -26$