You are in a bind here, sorry to break it to you.
First, Amsterdam is a great city. It's an adult playground, really. Food, sights, pot, canals, beer, art, night life, etc. It's a place to have fun and as we know, sex is the most fun of them all.
Second, there is a CONSTANT stream of tourists coming into and out of the city. And guess what? Old, boring, gray hairs are the minority of them. The majority of them are young people between 20-35, and they aren't coming there just to go to the Rijksmuseum or the Anne Frank Haus.
Third, women traveling with women friends are notorious for getting laid on vacation because "that doesn't count."
Fourth, they will party, a lot. In places with lots of other drunk and stoned people. They will get hit on. A lot. Plenty of cute guys with accents there who want to bang an American babe. She's going into the lion's den, basically.
Amsterdam is not London, Dublin, or Paris. That is, yes, someone could get picked up in one of those cities, but Amsterdam advertises its openness to drugs, sex, and rock-and-roll and young horny people from all over the world go there.
She will be tempted. She will have plenty of opportunity to get laid as much as she likes.
That's not to say that she will.
But you simply asked if you should be worried if she will. Yes, absolutely.
And you've only been dating 5 weeks? Probably not much of a bond there.
Blow up her text while she's gone, you'll drive right into Gunter's lap.
Not much you can do about it, really.
Sorry, I'm sure this won't help you sleep tonight or while she's gone, but don't ask a question you don't want an answer to.
Finally, as someone said above.... you'll never know. If she bangs a dude, she ain't telling you about it anyway.
Good luck with this man, you are going to need it.