The English language develop out of Germanic dialects that were brought to Britain during the course of the 5th and 6th centuries........
The main part of the sentence is:
The English language developed out of Germanic dialects.
This happened long ago in the past, so past tense.
(The rest of the sentence adds further information).
during the course of the 5th and 6th centuries ... By medieval times, this Germanic language had replaced the original Celtic language.
'by' indicates the end of a particular time period, that period being from 6th century, to Medieval times. So, we are discussing something that happened totally in the past, over a time period. The tense we use is Past Perfect.
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