Incorrect on ALL points. A test match does not last for five days, the permissable time to complete the match is 5 days.
There are very few test matches which finish on fourth day or earlier. When a match is a draw (and many are), of course it goes on for full five days. Even when one team wins, the match most of the time goes on into the fifth day. If the match is finished fourth day or earlier, that means one team was much stronger than the other team. E.g. England vs. India, or West Indies vs. Pakistan (in those days).
And of course a match can finish if a result is obtained before five days, what is the big deal there? The match is scheduled for five days. If a result is obtained the match is over. That applies not only to cricket, but too many other sports and games (e.g. chess, tennis, badminton etc.), that is only common sense.
But a test match is scheduled for five days, and most of them do go on for five days.
A test match is an unlimited overs form of cricket. So there is no minimum time that has to be played. The time is governed by the skill or lack thereof of the players. I've seen test matches that were over by mid-morning on the second day. A fielding captain having bowled out the opposition for a low score (day 1), then his team gaining a high innings will often declare to avoid the loss of more wickets & to force the follow on (day 1). The oppostion removed quickly in second innings, no need for the team that declared to take a second innings on day 2.
As for your comment about a draw, utter nonsense! I've never attended or seen a drawn cricket match. Very few cricket matches end in a draw.
And contrary to what you may think, a great many test matches end in a draw, at least they did 20 year ago, when I stopped following cricket. In a 5 match series, the typical score for winning team maybe 2 wins, 1 loss and two draws. I have seen series where 4 or even all 5 test matches ended in a draw. I cannot recall even one series here they had all five ended in other than a draw.
I suggest you look up some historical data on internet as to test series in the old days. You will find that a great many test matches ended up in a draw (they probably still do). For somebody who calls himself a cricket fan, you seem to be surprisingly ignorant of old days. A real aficionado would know something about cricket all the way from Don Bradman (have you heard of him)?