To find the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.
Given:
- Radius \( r = 5 \) inches
- Height \( h = 15 \) inches
- Using \( \pi = 3.14 \)
Now, plug the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (5^2) \times 15 \]
Calculate \( 5^2 \):
\[ 5^2 = 25 \]
Then substitute that back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 25 \times 15 \]
Now, calculate \( 25 \times 15 \):
\[ 25 \times 15 = 375 \]
Now substitute that back:
\[ V = \frac{1}{3} \times 3.14 \times 375 \]
Calculate \( 3.14 \times 375 \):
\[ 3.14 \times 375 = 1177.5 \]
Finally, divide by 3:
\[ V = \frac{1177.5}{3} = 392.5 \]
So, the volume of water the flower vase can hold is
\[ \boxed{392.5 \text{ cubic inches}} \]