Amsterdam layover

Yes, a very quick tour. The train from the the airport to Centraal Station is 20 minutes. From Centraal you can walk to down to Dam Square, then to the Anne Frank House or the Amsterdam Historical Museum, head back to Dam Square get a quick bite to eat, take a walk through the infamous Red Light District, and then back to Centraal Station for the train back to Schipohl.

You could take a canal tour also - they are only an hour.

Check the local boat/canal tours - or head over to the museums and back. A bike ride would be fun but maybe better for a full day if you want to explore. Check out the canal ride times in ricks book.

Amsterdam is one of the places where it is very easy to head into town to do some sightseeing to bridge a few hours of layover time. 5 hours is plenty of time to get a nice feel of the city.

However, if your flight arrives very early keep in mind that many attractions may not open till 9 or 10 am. I don't think boat tours are offered that early. That would still allow you to walk around a bit and have some breakfast. Not only a way to experience Amsterdam but also good against jet lag.

We just did this a few weeks ago and enjoyed our short visit. One bit of advice: if you lock up your bags, be sure to take them to the area your next flight is departing from. We put ours in the first lockers we saw before exiting, not realizing that the departure was from a different area, and had to circle through security/immigration twice to get our bags and make our way to the gate.
Be sure to be there 1.5 hours before departure. Schiphol herds people like sheep into the boarding area (corral)interviewing and double-checking bags of every passenger before anyone is let onto the plane. Enjoy your trip!

imo, spend the $$ and take a cab from schiphol. By the time you deplane, customs, baggage, etc you've already lost time. Figuring out the train, tickets isnt hard but it takes longer than getting a cab. It'll be about 35euro to CS, ~20 minute ride.
your time is money!!

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FYI The airport has a small museum BUT with really great paintings free a few years ago, you may have to ask where it is .

If you have a lot of carry-on, you can store it in a locker before you go thru passport control, 6 euros for a medium-sized locker. I saw a machine at the left side of the locker bank that changed bills to coins. You will need euros, though.