The volume \( V \) of a cone can be calculated using the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cone.
Given:
- Radius (\( r \)) = 5 inches
- Height (\( h \)) = 15 inches
- \( \pi \) = 3.14
Now, substitute the values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (5)^2 \times 15 \]
Calculating \( (5)^2 \):
\[ (5)^2 = 25 \]
Now, substitute this back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 25 \times 15 \]
Calculating \( 25 \times 15 \):
\[ 25 \times 15 = 375 \]
Now substitute this back into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 375 \]
Calculating \( 3.14 \times 375 \):
\[ 3.14 \times 375 = 1177.5 \]
Now substitute this back into the formula:
\[ V = \frac{1}{3} \times 1177.5 \]
Calculating \( \frac{1177.5}{3} \):
\[ \frac{1177.5}{3} = 392.5 \]
Therefore, the volume of water that the flower vase can hold is:
\[ \boxed{392.5} \text{ cubic inches} \]