Answer
$0.285\text{ cm}^3$
Work Step by Step
We convert carats to grams"
$5.0\text{ carats}\times 0.200\text{ g/carat}=1.00\text{ g}$
Then we determine the volume using the density of diamond ($3.51\text{ g/cm}^3$):
$\text{Volume}=\frac{1.00\text{ g}}{3.51\text{ g/cm}^3}\approx 0.285\text{ g/cm}^3$
