To calculate the standard deviation for the dataset \(3, 4, 5, 6, 7\), we will follow these steps:

1. Calculate the mean (\(\bar{x}\)) of the data. 
   \(\bar{x} = \frac{3 + 4 + 5 + 6 + 7}{5} = \frac{25}{5} = 5\)
2. Find the deviations of each data point from the mean and square each deviation.
   • \(3 - 5 = -2\quad \rightarrow \quad (-2)^2 = 4\)
   • \(4 - 5 = -1\quad \rightarrow \quad (-1)^2 = 1\)
   • \(5 - 5 = 0\quad \rightarrow \quad (0)^2 = 0\)
   • \(6 - 5 = 1\quad \rightarrow \quad (1)^2 = 1\)
   • \(7 - 5 = 2\quad \rightarrow \quad (2)^2 = 4\)
3. Calculate the average of these squared deviations. 
   \(\frac{4 + 1 + 0 + 1 + 4}{5} = \frac{10}{5} = 2\)
4. The standard deviation (\(\sigma\)) is the square root of the variance. 
   \(\sigma = \sqrt{2}\)

Therefore, the standard deviation of the given dataset is \(\sqrt{2}\), which matches the correct answer option provided.