Five hours to kill in Amsterdam

Get a hold of RS's Amsterdam book and do some of the walks (or photocopy them from the library so you don't have to lug the book around just for 5 hours). You get a scenic tour that covers a lot of ground and it is relatively cheap. But if you want to do more than stroll, take a peek at one of the many museums. I enjoyed the heck out of the Rijks Museum and Van Gogh museum. Transportation from the train station can get you there in a jiffy. Perhaps a canal cruise would fit into the time you have allotted.

Is that 5 hours from when your first plane lands and the next one takes off? Or have you got 5 hours after taking into account the time to de-plane and then check in for your next flight?

If it's the first one, then I would suggest staying within Schipol airport. It's got some good shops and last time I was there it had a permanent Rembrandt exhibition.

The transport into Amsterdam from the airport is fast, but unless you have 5 completely clear hours, you won't get long in Amsterdam proper, which is probably why you asked for tours near the airport. I don't know of anything near the airport.

Schipol seemed to have a lot to do, including a small outpost of the Rijksmuseum, a large Escher piece, and lots and lots of shops. But if you really want to leave the airport, and it's a weekday morning, maybe check out the Aalsmeer Flower Auction, the largest flower auction in the world.

The area near the airport is about as industrial as can be... not much to be found there.

For inner-European flights you don't need a 2 hour check-in, an hour is fine as well. That would leave you enough time to explore a bit of the city considering that the train into town takes only 15 minutes. It's a different story if you are returning to the US when security might take much longer.

When do you arrive? If it's early in the morning you need to take into account that many museums might not be open till 10 am. But you could use that time to wander around and have breakfast at a nice cafe overlooking a canal. If you want to see the Anne Frank House reserve tickets online in advance. Otherwise you might end up standing in line for a long time between all those school classes who want to get in as well. Line-ups at the van Gogh museum are usually not a concern as the place can handle much larger crowds.

Van Gogh Museum, definitely. The guided river cruise is also good for seeing a lot of the city quickly and leisurely.