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Is the equation $5! \cdot 4!$ correct?

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    Looks like you got the help you wanted, great! For future reference, consider putting more detail into your thought process in the question. This has two advantages: 1) People are more inclined to help when someone has shown they're not just interested in the answer 2) Any conceptual errors may be noticed by someone and they can help you with that too – 2017-02-15

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Number of ways to arrange the $5$ girls: $5!$.

Number of ways to place the $4$ boys, unordered, around the $5$ girls: $5$.

Number of ways to arrange the $4$ boys: $4!$.

Thus the answer is: $5 \cdot 5! \cdot 4! = 5!\cdot 5! = (5!)^{2}$.

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    You mixed up the boys and the girls, but based off your answer, I would assume there are 5! x 5! ways? – 2017-02-15
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    Woops! I'll edit the answer with the correct numbers. You are correct, $5! \cdot 5!$ is the answer. – 2017-02-15
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If you think of the girls as one unit (since they can't be separated), there are $5!$ ways to permute the boys and girls. Within the unit of girls, there are $5!$ places in which they can stand, so it should be $5!\cdot 5!$.