According to the formula, If pipe A  and B fills a tank in x and y hours respectively, but a third pipe C empties the full tank in z hours then full tank will be filled in $\frac{\mathrm{xyz}}{\mathrm{yz}+\mathrm{xz}-\mathrm{xy}}$ hours.

So,

$$\begin{gathered} \frac{5\times 6\times 12}{\left(5\times 12\right)+\left(6\times 13\right)-\left(5\times 6\right)} \\ =\frac{360}{72+60-30}=\frac{360}{102}=3\frac{9}{17} \mathrm{hours} \end{gathered}$$

The tank will be filled in $3\frac{9}{17}$ hours when all the pipes are opened simultaneously.

Hence option C is correct