Yes, they can travel within forests
Depending on the forest tree type, trees can reach much higher altitudes than what your giants are tall, so the risk of stumbling on a branch is quite low. Also, some trees give of branches only at higher altitude, making only the trunk an issue. To give you three instances of high trees forests :
- The Pacific Northwest forest is quite known for their big, big trees. Plus, the branches start to really span only at a high level.
It's your lucky day! You can estimate how big your giant would look like with these two hikers there :). Photo from Wikimedia Commons
- The Landes forest in France's southwest is composed of a vast majority of Pinus pinaster, or maritime pines in plain English. They usually range between 20 and 30m, and the branches really start to pick up at ~half of it, so quite above your 5-6m giants. Please note it was man-made.
- If you're more leafy than needly, some deciduous forests can do the job. Here's the temperate forest at the Othe's domain. Not the best, but it's still livable.
See the '6' and green line mark on the front tree in the centre? These paints usually stand at around 1 to 1.5m, so you can make a rough scale with it. Photo from Wikimedia Commons
Also, I guess that wasn't what you had in mind, but if you take your definition of "forest" further, thorn forests in semi-arid areas can be a choice, too, since trees can be quite scarce there. However, take some good boots to protect yourself from thorns, there are a lot of those.
I kinda cheated. In order to explain why, you have to know that forests actually live in cycles. Indeed, there's a constant competition for sunlight among vegetation : First bushes come in, then frail, short-lived trees like birch or willow trees, then only the taller, stronger and wider ones you want come in. The pictures above are taken at the later stages, and I've skipped the early stage, bushland photos.
What should you understand from this? First, that your world forests should likely be 200 years old or more in order to reach the later stages. That's around how old the Landes Forest is. Then... In a single woodland region, not all areas will be crossable : Depending on many conditions (soil nutriments and acidity, wildfires...), some areas will be less "developped" than others, leading to smaller trees that can block the way to your giants. The same actually happens to us, humans : The only travelers in some parts of forests are small animals like rabbits and rodents, the bushes being too dense for us.
Most if not all animals make trails in woodlands, and if they're sentient and don't like to beat around the bush they do so even more. That's both a nice thing, a risk and an opportunity for you. It's good because trails make it much easier to travel in any land and regardless of size. It's a risk because if your giants existence have to be unproven for commonfolk -like Bigfoot or Nessy-, evident traces of 3m wide dirt roads with big feet marks will move them into reality. But it's also an opportunity because people, when finding the road, will take the chance to exagerate the proportions of the giants when retelling the myth. So think about it 🐶!