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For the first flower she has a choice of 15. For the second 14 (15 minus the one that was already used). For the third 13, and so on.
Each of the first 15 can be match with any of the second 14. Any of the first pairs can be matched with ant of the third 13 and so on.
This gives us
Number of Selections = Choices for Flower 1 x Choices for Flower 2 x Choices for Flower 3 x Choices for Flower 4 x Choices for Flower 5
You could also calculate this as the permutation