1. **State the problem:** We need to find the length of a straw placed diagonally inside a rectangular box with dimensions 5 inches by 5 inches by 8 inches. The straw stretches from the bottom left corner to the top right back corner. 2. **Formula used:** The diagonal $d$ of a rectangular box with length $l$, width $w$, and height $h$ is given by the 3D Pythagorean theorem: $$d = \sqrt{l^2 + w^2 + h^2}$$ 3. **Apply the formula:** Here, $l = 5$, $w = 5$, and $h = 8$. 4. **Calculate the squares:** $$5^2 = 25$$ $$5^2 = 25$$ $$8^2 = 64$$ 5. **Sum the squares:** $$25 + 25 + 64 = 114$$ 6. **Find the diagonal length:** $$d = \sqrt{114}$$ 7. **Simplify the radical if possible:** 114 factors as $2 \times 3 \times 19$, none are perfect squares, so $\sqrt{114}$ is already in simplest radical form. **Final answer:** The length of the straw is $\boxed{\sqrt{114}}$ inches.