[Tomisimo]

Here's my take off the cuff:

Of the five words, smart and intelligent are the closest in meaning, the later normally being used in higher registers than the former. Wisdom implies intelligence with extra experience. A clever person is not only smart, they also have a certain flair when expressing that intelligence. A shrewd person is smart in a defensive manner.

Intelligent/smart: You know that driving a car at 150 mph is dangerous.
Wise: You decide not to drive a car at 150 based on the above fact.
Clever: You decide to travel by high-speed train to make the needed journey instead of risking a high-speed car trip.
Shrewd: You research which train car has fewer passengers, and ask for a ticket placing you there so you have a better chance of getting some sleep during the trip.