To solve this problem, we need to find five prime numbers arranged in ascending order such that the ratio of the product of the first three numbers to that of the last three numbers is 35:323. We then determine the difference between the smallest and largest numbers.

Let's denote the prime numbers by \(p_1, p_2, p_3, p_4, p_5\).

The given ratio is:

\(\frac{p_1 \times p_2 \times p_3}{p_3 \times p_4 \times p_5} = \frac{35}{323}\)

Simplifying the ratio on the right-hand side gives:

35 can be written as \(5 \times 7\) and 323 as \(17 \times 19\).

So, the equation becomes:

\(\frac{p_1 \times p_2}{p_4 \times p_5} = \frac{5 \times 7}{17 \times 19}\)

This implies that \(p_1 = 5\), \(p_2 = 7\), \(p_4 = 17\), and \(p_5 = 19\). We need to find the third number \(p_3\), which must also be a prime number and common to both products.

Some possible options for \(p_3\) that fit the criteria are \(11, 13\). After testing these:

If \(p_3 = 11\), the numbers are: 
\(p_1 = 5\), \(p_2 = 7\), \(p_3 = 11\), \(p_4 = 17\), \(p_5 = 19\).

Now, let's calculate the difference between the smallest and largest numbers:

Difference = \(19 - 5 = 14\).

Hence, the correct answer is 14.