1. For a simple pendulum in SHM, one complete oscillation takes time $T$.

2. Starting from the mean position, the motion timeline is:

   • Mean to extreme: $\dfrac{T}{4}$
   • Extreme back to mean: $\dfrac{T}{4}$ So, every half oscillation takes $\dfrac{T}{2}$.

3. We need the time for $\dfrac{5}{8}$ oscillations.

4. Since 1 oscillation takes time $T$, the time for $\dfrac{5}{8}$ oscillations is directly: $t = \frac{5}{8}T$

5. Therefore, $\frac{\alpha}{\beta}T = \frac{5}{8}T$ Hence, $\alpha = 5, \quad \beta = 8$

6. So the required value is: $\boxed{5}$

7. Comparison with stored answer:

   • Derived answer = $5$
   • Stored correct answer = $7$
   • These do not match.

The phrase "starting from mean position" does not change the result, because the fraction of an oscillation is defined in terms of the full period, and $\dfrac{5}{8}$ of a complete oscillation always takes $\dfrac{5}{8}T$.