Answer
$ d=-5 \sin (\dfrac{ 4\pi}{5}) t $
Work Step by Step
Amplitude, $ A=-5$
(negative because the object is moving down initially.)
Given: $ Period =2.5$
Now, period, $ P=\dfrac{2 \pi}{\omega} \implies \omega =\dfrac{2 \pi}{2.5}=\dfrac{ 4\pi}{5}$
So, $ d=A \sin \omega t=-5 \sin \dfrac{ 4\pi}{5} t $
