Let the random variable \(X\) represent the time taken to swim 100 metres. \(X\) follows a normal distribution with mean \(\mu = 62\) and standard deviation \(\sigma = 5\).

We need to find \(P(56 < X < 66)\).

Standardize the variable using the formula:

\(Z = \frac{X - \mu}{\sigma}\)

For \(X = 56\):

\(Z = \frac{56 - 62}{5} = -1.2\)

For \(X = 66\):

\(Z = \frac{66 - 62}{5} = 0.8\)

Thus, \(P(56 < X < 66) = P(-1.2 < Z < 0.8)\).

Using the standard normal distribution table, find:

\(\Phi(0.8) = 0.7881\)

\(\Phi(1.2) = 0.8849\)

Therefore, \(P(-1.2 < Z < 0.8) = \Phi(0.8) + \Phi(1.2) - 1 = 0.7881 + 0.8849 - 1 = 0.673\).