Explanation

Modulo 5: 111 ≡ 1, so 111²²² ≡ 1. Since 2⁴ ≡ 1 (mod 5) and 333 = 4·83+1, 222³³³ ≡ 2³³³ ≡ 2 (mod 5). Since 3⁴ ≡ 1 (mod 5) and 444 = 4·111, 333⁴⁴⁴ ≡ 1 (mod 5). The sum is 1+2+1 = 4 (mod 5) — option D.