I'm not sure how long you have been here, but here is our story:
We were in a similar position when we arrived 2 years ago with a 5 and 7 year old. Our 5 year old had completed a first year in school and had started his second year. We considered home schooling, but decided to place him in kindergarten (which some might think was a step backwards). Our thought process was that he would be able focus on his Portuguese language, cultural and social skills. If we home schooled we would be in the same position a year later, where he would still be academically ahead of the Portuguese learning curriculum.
The classes were not taxing, instead they were thoroughly enjoyable and he adapted far quicker than our 7 year old. We never once had to encourage him to go to school. He did get bored occasionally, but I think that helped him adapt to the pace of learning here plus we made sure he was active outside of school (Karate, bike riding etc).
He is in the top 10% in his class, has no issues with any of the topics, and we keep his English skills topped up at home with lots of reading books and letter-writing to grandparents.
Hope this helps