I second the motion of blightyboy. I did that on my first landing at Heathrow. I had a short layover and hired a cabbie to give me a tour of London.

For a first timer to Amsterdam 5h45m is cutting it close, especially with the security these days. My experience on USA bound flights from Schiphol in the past few years is that there is an additional detailed security check at the gate. That is a one hour line.

Unless you like cliff hangers, with you doing the hanging, don't do Amsterdam in this time frame.

Migo-I don't think that anyone who has a VERY limited amount of time to take a first-time look through a city is going to want to then spend that time going to a museum! That very thought is ridiculous!

However, hetismij's suggestion to take the one hour canal ride is quite enjoyable, well worth it, and doable-you can catch that canal ride right outside the Centraal station.