If Mark and Luke were independent of each other, this would be a puzzling contradiction that we would need to resolve if we ever wanted to know in what order events really occurred. However, it is now the strong consensus of scholars that Luke was based on Mark's Gospel, with further sayings material taken from the hypothetical 'Q' document. Some of the reasons for this conclusion are found here, although there are some more technical reasons that scholars use and which are not listed in those answers. Adam Winn (The Purpose of Mark's Gospel, page 1) says the theory of Markan priority is one of the few that has reached a high level of consensus among New Testament interpreters.
The (anonymous) author of Luke's Gospel states that his community received the gospel from others, the earliest of whom he assumes were eyewitnesses, confirming the above conclusion:
Luke 1:1-2: Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us, Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word;
From this, we can establish that Luke 4:44-5:11 was copied from Mark 1:16-21. Modern historians expect events to be recorded exactly as they happened, but this was not always the case in ancient times. As far as we can know, the sequence of events should be as established in Mark's Gospel.