To determine how many ways the top 5 awards can be allocated from a field of 20 athletes, we first recognize that this is a permutation problem, since the order in which athletes finish is important (i.e., 1st, 2nd, 3rd, 4th, and 5th place).
The number of ways to choose and arrange 5 athletes out of 20 can be calculated using the permutation formula:
\[ P(n, k) = \frac{n!}{(n-k)!} \]
where:
- \( n \) is the total number of athletes (20),
- \( k \) is the number of top positions to fill (5).
Plugging in the values:
\[ P(20, 5) = \frac{20!}{(20-5)!} = \frac{20!}{15!} \]
To simplify \( \frac{20!}{15!} \):
\[ \frac{20!}{15!} = 20 \times 19 \times 18 \times 17 \times 16 \]
Now we will calculate this product step-by-step:
- \( 20 \times 19 = 380 \)
- \( 380 \times 18 = 6840 \)
- \( 6840 \times 17 = 116280 \)
- \( 116280 \times 16 = 1860480 \)
Therefore, the number of ways to allocate the top 5 awards to the 20 athletes is:
\[ \boxed{1860480} \]