The number of students to be arranged in the front row is $k = 5$.
We want to arrange 5 students out of 23 students in the front row.
The order of the students matters, so we use permutations.
The number of ways to arrange 5 students out of 23 students is given by the permutation formula:
$$P(n, k) = \frac{n!}{(n-k)!}$$
In this case, $n = 23$ and $k = 5$.
$$P(23, 5) = \frac{23!}{(23-5)!} = \frac{23!}{18!} = 23 \times 22 \times 21 \times 20 \times 19$$
$$P(23, 5) = 23 \times 22 \times 21 \times 20 \times 19 = 4903140$$
Therefore, there are 4,903,140 ways to arrange 5 students in the front row of the classroom from a total of 23 students.
The number of ways to arrange 5 students from 23 students in the front row is given by the permutation formula:
$$P(23, 5) = \frac{23!}{(23-5)!} = \frac{23!}{18!} = 23 \times 22 \times 21 \times 20 \times 19$$
Calculating the product:
$23 \times 22 \times 21 \times 20 \times 19 = 4903140$
Thus, there are 4,903,140 ways to arrange 5 students in the front row of the classroom.
Final Answer: The final answer is $\boxed{4903140}$