The third proportional to $6\dfrac{1}{4}$ and 5 is

1. 4

2. $7\dfrac{1}{2}$

3. 3

4. none of these

Let the third proportional be x.

Hence, the numbers $6\dfrac{1}{4}$, 5, x are in continued in proportion.

$\therefore \dfrac{25}{4} : 5 : : 5 : x \\[0.5em] \Rightarrow \dfrac{\dfrac{25}{4}}{5} = \dfrac{5}{x} \\[0.5em] \Rightarrow \dfrac{25}{20} = \dfrac{5}{x} \\[0.5em] \Rightarrow x = 5 \times \dfrac{20}{25} \\[0.5em] \Rightarrow x = 4.$

∴ Option 1 is the correct option.