DC2 is YR, also 5, and started piano lessons at 4; the teacher works at the school, also teaches DD (7) and said she'd take him despite all the school music teachers also having a general rule not to take below 7, so it is definitely worth asking re individual circs. Her explanation was that 7 is usually the age around which children can read sufficiently and pay attention for long enough to get anything out of it, but she knew DS could read/concentrate as she'd seen him read chapter books in single sittings.
However, what neither of us had considered was that as he progressed, his size would be a problem! He was going through her usual teaching books quite quickly, but he's hit a stumbling block with more and more black keys - he has to lift his entire arm up and over the whites to get to the blacks and he can't move his whole arm fast enough to get the fluency. The teacher has now found books from decades ago when they started teaching at a younger age and there are only occasional black keys, but clearly size is a barrier to progress and he would learn faster when older/bigger (he's small for age though).
The violin teacher at school has also agreed to take him on. Here size is less of an issue, as he needs a 1/10 instrument and they can be sourced relatively easily from instrument hire companies (so we don't have to keep buying new ones as he grows).
Soooo... my advice is to assess your DS and his reading ability and concentration (reading is apparently because if they're still learning to read, it can be quite difficult to also learn to read music at the same time, concentration is obvious for 20 or 30 min one-to-one lessons!), then also consider his size and what instrument might suit. And speak to the music teachers personally, listen to what they say. In the meantime, just let him play and listen to the sounds he's making himself - assuming he's also YR, next year is going to get a lot more demanding and he may just be too tired for music lessons on top of school.