Let \(S\) be the set of permutations of the sequence \(2, 3, 4, 5, 6\) for which the first term is not \(2.\) A permutation is chosen randomly from \(S.\) The probability that the second term is \(5\) is given by \(\dfrac{a}{b}\) (in lowest terms). What is \(a+b?\)

(A) 5
(B) 6
(C) 11
(D) 16
(E) 19

Answer: E

Source: Veritas Prep