projected_data = np.dot(centered_data, sorted_eigenvectors[:, :5])

This line of code projects the centered data onto the first 5 principal components (sorted_eigenvectors) using matrix multiplication (np.dot). The resulting projected_data matrix will have the same number of rows as the original centered_data matrix, but only 5 columns corresponding to the 5 principal components. This step is often used for dimensionality reduction or feature extraction, as it allows us to represent the data in a lower-dimensional space while preserving as much of the original variance as possible.