Given SHM equation

$y = 5(\sin 3\pi t + \sqrt{3}\cos 3\pi t)\ \text{cm}$

Rewrite it as:

$y = 5\sin 3\pi t + 5\sqrt{3}\cos 3\pi t$

Compare with standard form

A general SHM can be written as:

$y = a\sin \omega t + b\cos \omega t$

whose amplitude is:

$A = \sqrt{a^2+b^2}$

Here,

$a = 5, \qquad b = 5\sqrt{3}$

Therefore,

$A = \sqrt{5^2 + (5\sqrt{3})^2}$ $A = \sqrt{25 + 75}$ $A = \sqrt{100} = 10\ \text{cm}$

Find angular frequency

The argument of sine and cosine is $3\pi t$, so:

$\omega = 3\pi\ \text{rad/s}$

Find time period

$T = \frac{2\pi}{\omega} = \frac{2\pi}{3\pi} = \frac{2}{3}\ \text{s}$

Match with options

Amplitude $= 10\ \text{cm}$ and time period $= \dfrac{2}{3}\ \text{s}$.

So the correct option is:

$\boxed{\text{D}}$