Answer: A. $-111$

Explanation:

$1$ . Set up the equation using the given information:

   - We are given that $f(a) = -19$ .

   - Substitute 'a' into the function definition: $f(a) = \dfrac{a+16}{5}$ .

   - Therefore, we can set the two expressions for $f(a)$ equal to each other: $\dfrac{a+16}{5} = -19$.

$2$ . Solve the equation for a:

   - Multiply both sides by $5$ to eliminate the denominator:

     $a + 16 = -19 \times 5$

     $a + 16 = -95$

   - Subtract $16$ from both sides:

     $a = -95 - 16$

     $a = -111$

$3$ . Conclusion:

   - The value of a is $-111$ , which corresponds to option A.