To solve this problem, we can use two methods:

Method 1:

First, arrange the 5 men. There are 5! ways to do this.

\(5! = 120\)

Now, consider the gaps between the men where the women can be placed. There are 6 gaps (before the first man, between the men, and after the last man).

We need to choose 2 out of these 6 gaps to place the women, which can be done in \(^6P_2\) ways.

\(^6P_2 = 6 \times 5 = 30\)

Thus, the total number of ways is:

\(5! \times ^6P_2 = 120 \times 30 = 3600\)

Method 2:

Calculate the total number of arrangements without any restrictions, which is 7! (since there are 7 people).

\(7! = 5040\)

Calculate the number of arrangements where the women are together. Treat the two women as a single unit, so we have 6 units to arrange (5 men + 1 unit of women).

There are 6! ways to arrange these units, and within the unit of women, the 2 women can be arranged in 2! ways.

\(6! \times 2! = 720 \times 2 = 1440\)

The number of arrangements where the women are not together is:

\(7! - (6! \times 2!) = 5040 - 1440 = 3600\)

Both methods give the same result: 3600 ways.