For an ideal gas, the standard molecular speeds are:

• Average speed: $v_{\text{avg}}=\sqrt{\frac{8RT}{\pi M}}$

• RMS speed: $v_{\text{rms}}=\sqrt{\frac{3RT}{M}}$

Hence, their ratio is

$\frac{v_{\text{rms}}}{v_{\text{avg}}} = \sqrt{\frac{3RT/M}{8RT/(\pi M)}} = \sqrt{\frac{3\pi}{8}}$

According to the question,

$\frac{v_{\text{rms}}}{v_{\text{avg}}} = \sqrt{\frac{\alpha+5}{\alpha}}$

Therefore,

$\sqrt{\frac{\alpha+5}{\alpha}} = \sqrt{\frac{3\pi}{8}}$

Squaring both sides,

$\frac{\alpha+5}{\alpha} = \frac{3\pi}{8}$

Using $\pi=\frac{22}{7}$,

$\frac{\alpha+5}{\alpha} = \frac{3}{8}\cdot\frac{22}{7} = \frac{66}{56} = \frac{33}{28}$

Now solve for $\alpha$:

$\frac{\alpha+5}{\alpha}=\frac{33}{28}$

$28(\alpha+5)=33\alpha$

$28\alpha+140=33\alpha$

$140=5\alpha$

$\alpha=28$

Therefore, the correct option is:

$\boxed{28}$

So, option B is correct.