Why 了 in 走+time+就到了？
了 at the end of a sentence is (most often) a modal particle that indicates change of state. 

In your example sentence:


  ... 走五分钟就到了


it marks the change of state that occurs when, after walking for five minutes (original state, walking), you arrive at your destination (change of state, arrived).

This use of 了 is common in: 


expressions involving time, because the passing of time often involves state changes: 我等了一个小时的车了, "I waited (original state) the bus one hour (change of state, not waiting anymore)"
commands, as they imply a change of state as soon as the command is executed: 你闭嘴了, "Shut up!" (talking, original state, to not talking, change)
'going to' forms with 要～了 or 快～了, as they imply an imminent change in the future: 今天要下雨了 "It's going to rain, today" (not raining, original state, to raining, change)


You can also find a nice explanation of different flavors of 了 here.