Given,

$7\frac{7}{12}\times 6\frac{7}{19}÷19\frac{1}{3}=?$

It can be approximated as

$$\begin{gathered} = \frac{91}{12}\times \frac{121}{19}÷\frac{28}{3}=? \\ = \frac{90}{12}\times \frac{120}{20}\times \frac{3}{30}=? \\ = \frac{45}{10}=? \end{gathered}$$

= 4.5 = 5

Hence, Option D is correct.