To find the volume of a hemisphere, we can use the formula for the volume of a sphere and then take half of that volume.
The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
Since Aimee's hemisphere has a diameter of 5 cm, we can find the radius by dividing the diameter by 2:
\[ r = \frac{5 \text{ cm}}{2} = 2.5 \text{ cm} \]
Now, we can calculate the volume of the full sphere using the radius:
\[ V = \frac{4}{3} \pi (2.5)^3 \]
Calculating \( (2.5)^3 \):
\[ (2.5)^3 = 2.5 \times 2.5 \times 2.5 = 15.625 \]
Now substituting this value into the volume formula:
\[ V = \frac{4}{3} \pi \times 15.625 \]
Calculating \( \frac{4}{3} \times 15.625 \):
\[ \frac{4}{3} \times 15.625 = \frac{62.5}{3} \approx 20.8333 \]
Now we can multiply by \( \pi \):
\[ V \approx 20.8333 \times \pi \approx 20.8333 \times 3.14159 \approx 65.4498 \]
Since we are interested in the volume of the hemisphere, we take half of this volume:
\[ V_{\text{hemisphere}} = \frac{1}{2} \times 65.4498 \approx 32.7249 \]
Finally, rounding to the nearest hundredth, the volume of the hemisphere is:
\[ \boxed{32.72} \text{ cm}^3 \]