Explanation

Working mod 29, 16 ≡ −13 and 15 ≡ −14. Since the exponent 5 is odd, (−13)⁵ ≡ −13⁵, so 13⁵+16⁵ ≡ 0 (mod 29); likewise 14⁵+15⁵ ≡ 0. The total remainder is therefore 0 (option D).