Answer:
There are 3003 different ways to choose the 5 flowers.
Explanation:
For solving this question we need to understand the concept of combination. The combination can be calculate as:

This value give as the number of ways in which we can select k elements from a group of n elements and the order in which this elements are chosen doesn't matter.
Replacing n by 15 and k by 5, we get:

15C5=3003
So, there are 3003 different ways to choose the 5 flowers from a group of 15.