fun things to do with 5 and 10 year old in Iceland

Can only tell that you are too late to see puffins for sure. They are permanently at sea after breeding.

If they like animals, you could visit the Slakki petting zoo or the Reykjavík Park and Zoo. The latter also has some rides, a go-cart track and other activities.
As for thermal pools, the one in Selfoss is nice, with slides, a paddling pool, sauna, hot tubs, etc. and access is free for the kids. In Reykjavík I recommend the Árbær pool, which has a large water slide and an amazing view over the city. The one in Akureyri is also nice, and has a water slide. The pool in Hofsós doesn't have a slide or much to amuse kids, but is worth visiting for the view.

Thank you very much for your responses!

As an example, Ishestar are one of the best known tourist horse riding operators serving the Reykjavik tourist market, and they offer a children's activity.
http://www.ishestar.is/tours/family-adventure
But there are many little places all around Iceland offering riding and you may find something more flexible/cheap as you are passing.

In general in Iceland, they don't like putting the car park too near the sight, so seeing curiosities often involves short walks. So in fact many of the standard curiosities are, unintentionally, well constructed as little hikes for children with a reward to encourage them of seeing the curiosities. For example, Gullfoss and Dettifoss are both a bit of a hike from the car park, especially the latter. Skaftafell has short hikes to see nice things, etc. Thingvellir, etc.

At Hveragerdi, you can walk up a valley to bathe in a warm stream - though it's probably a good hour each way with a 5 year old, providing you drive as close as you can. There are plenty of other curiosities around. There's also a large lavatube just off the road to Thorlakshofn, which may entertain children. More big lavatubes in the Borgarnes area.

I would try and stay at least a couple of days at Myvatn. There are a lot of curiosities to see there with the typical walks to explore them. Thinks like bubbling mud go down well with kids, but also climbing cinder cones, running around pseudocraters, exploring weird lava formations (both Dimmuborgir at Myvatn, but also Hljodaklettar on the road from Dettifoss to Asbyrgi, which I think is a 2wd road these days, though it still isn't paved).

Thank you iviehoff, this is very useful!

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