To solve the problem of calculating the number of ways to select 5 elements from 10 elements where order matters, we use permutations.

Key Concept: Permutations

When order matters, the number of ways to choose (k) elements from (n) elements is given by the permutation formula:
[P(n, k) = \frac{n!}{(n - k)!}]

Calculation

For (n = 10) and (k = 5):
[P(10,5) = \frac{10!}{(10-5)!} = 10 \times 9 \times 8 \times 7 \times 6 = 30240]

Answer: (\boxed{30240})

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