1. We start by stating the problem: Calculate $$\frac{(862 + 321) \times 66}{(368 + 810)} \bmod 5$$. 2. First, compute the sums inside the parentheses: $$862 + 321 = 1183$$ $$368 + 810 = 1178$$ 3. Substitute these values back into the expression: $$\frac{1183 \times 66}{1178} \bmod 5$$ 4. Calculate the numerator: $$1183 \times 66 = 78078$$ 5. Now the expression is: $$\frac{78078}{1178} \bmod 5$$ 6. Perform the division: $$\frac{78078}{1178} = 66.3$$ (approximately) 7. Since the division is not an integer, we interpret the problem as: Calculate $$((862 + 321) \times 66) \bmod ((368 + 810) \times 5)$$ or calculate the modulo after multiplication and division separately. 8. Alternatively, calculate the modulo of numerator and denominator separately: Calculate $$78078 \bmod 5$$ and $$1178 \bmod 5$$. 9. Calculate: $$78078 \bmod 5 = 78078 - 5 \times \cancel{15615} = 3$$ $$1178 \bmod 5 = 1178 - 5 \times \cancel{235} = 3$$ 10. Now the expression becomes: $$\frac{3}{3} \bmod 5$$ 11. Simplify the fraction: $$\frac{\cancel{3}}{\cancel{3}} = 1$$ 12. Finally, calculate modulo 5: $$1 \bmod 5 = 1$$ Answer: $$1$$